CaltechDATA: Monograph
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A Caltech Library Repository Feedhttp://www.rssboard.org/rss-specificationpython-feedgenenThu, 28 Mar 2024 11:14:35 -0700Stability and supersymmetry
https://resolver.caltech.edu/CaltechETD:etd-12092004-161650
Year: 1977
DOI: 10.7907/X6XZ-AX26
NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document.
PART I
A complete account of a perturbative investigation of ground state instability is presented for a massless theory involving scalar, pseudoscalar, and Majorana spinor fields. The effective potential, dimensional regularization, and renormalization group formalisms are briefly reviewed and then applied in detail to show the semiclassical vacuum of the model is unstable due to radiative corrections when the (pseudo)scalar self-interaction strength, f, is less than the fermion-(pseudo)scalar coupling, [...]. Models with stable ground states are found when [...], and when [...] supersymmetric theory is obtained. The supersymmetric case is thus encountered as a boundary between stable and unstable models. This result is discussed and is conjectured to be a general feature of supersymmetric theories. All perturbative calculations in the analysis are methodically carried out to the level of two-loop Feynman diagrams, and to this level, a variety of renormalization prescriptions are considered. The correlation of the various ultraviolet divergences for the supersymmetric model is explicitly demonstrated and shown not to hold in the general theory.
PART II
Renormalization group analysis is used to show the supersymmetric point in the effective coupling constant space is an unstable fixed point for several model gauge theories. The physical significance of this result is discussed in terms of the stability of the semiclassical ground state. In perturbation theory the supersymmetric point appears to be surrounded by regions in the coupling space representing three classes of theories: class one consists of theories for which the effective potential V has no apparent lower bound for large (pseudo) scalar field expectations; class two theories have lower bounds and radiatively induced absolute minima for V with nonzero field expectations; class three theories apparently have an absolute minimum of V at the origin of field space. Thus radiatively induced breaking of gauge invariance occurs for theories in classes one and two, but perturbatively the class one theories appear to have no ground states. Class three theories have ground states in which all gauge invariance remains intact. For the supersymmetric limits of the models examined the origin is known to be neutrally stable in field space, permitting an ambiguous breakdown of gauge invariance but not supersymmetry. This phenomenon is discussed in some detail. Calculations are performed in both Lorentz covariant and noncovariant gauges with a detailed comparison between gauges of the relevant one-loop diagrams. A null-plane limit of the noncovariant gauges is argued not to exist.
https://resolver.caltech.edu/CaltechETD:etd-12092004-161650Extended Supergravity with a Gauged Central Charge
https://resolver.caltech.edu/CaltechETD:etd-12022004-160245
Year: 1979
DOI: 10.7907/X6KP-V369
<p>We construct a Lagrangian for the massive scalar multiplet, locally invariant under two types of spinorial transformations (N=2 supersymmetry). Our theory is based on the coupling of the global supermultiplet to N=2 supergravity and corrections generated iteratively in powers of Newton's constant. Consistency of the theory requires the vector field of supergravity to gauge the central charge represented in the massive sector of the multiplet. The same vector may alternatively gauge the internal 0(2) symmetry of the two supersymmetry generators. Furthermore, it may even gauge a linear combination of the generators of these two groups; we indicate the grounds for this compatibility.</p>
<p>We discuss the hierarchy of internal symmetries characterizing each sector of the theory, ranging from U(1)xSU(2)xSU(2) down to 0(2)x0(2). This internal symmetry imposes tight constraints on the system. For instance, the nonpolynomial structure of the spinless fields at hand is considerably more restricted than that present in the general simple supersymmetric (N-1) theory. Furthermore, the vector field is forced to couple to the matter fields with gravitational strength, to the effect that the resulting Coulomb potential exactly cancels against the Newtonian potential of gravity, in the static limit.</p>
<p>Our theory may be also viewed as a truncation of N=8 supergravity theory, compatibly with the SO (8) breakup scheme into SU(3)xU(1)xU(1). The potential of the spinless fields present has a local minimum at the origin, but further off it is not even bounded from below. However, we point out some indications that the tunneling out of the supersymmetric, metastable vacuum is negligibly small.</p>https://resolver.caltech.edu/CaltechETD:etd-12022004-160245Use of Superspace Geometry to Find All Supergravity Theories: Case of N = 4 and SO(4) Symmetry
https://resolver.caltech.edu/CaltechETD:etd-12072004-143533
Year: 1983
DOI: 10.7907/PC47-EM20
<p>The main subject of this thesis is the study of the N = 4 supergravity theories. Superspace geometry is used to search for all N = 4 supergravities with at least SO(4) global symmetry. It is found that the general solution to the unconstrained Bianchi Identities, with the field content of N = 4 supergravity, are equivalent to the known SO(4) and SU(4) supergravities up to field redefinitions. Therefore the field content determines uniquely the N = 4 theories and further constraints are not necessary.</p>
<p>The SO(4) supergravity is gauged with two coupling constants and a new theory with positive cosmological constant and spontaneous breaking of the four supersymmetries is found. The presence of scalar fields in the kinetic term of the vectors is seen to make the values of the physical gauge coupling constants depend on the choice of vacuum.</p>https://resolver.caltech.edu/CaltechETD:etd-12072004-143533Topics in Supersymmetry Theory: 1. A Superspace Action for Ten-Dimensional Supersymmetric Yang-Mills Theory in Terms of Four-Dimensional Superfields; 2. Gauge Groups for Type-I Superstrings
https://resolver.caltech.edu/CaltechTHESIS:10232019-170411829
Year: 1983
DOI: 10.7907/qrfw-nf31
This thesis is an account or most of the work that I did in Supersymmetry and Supergravity over the last two years. It deals with two major topics. the construction of a new superspace action for ten-dimensional supersymmetric Yang-Mills theory in terms of four-dimensional superfields. and the classification of the gauge groups allowed at the classical level in the type-I superstring theory. In addition, it contains a discussion of work that I did showing the uniqueness of supergravity in eleven dimensions and the uniqueness of the free Rarita-Schwinger action for massless and massive spin-³/₂ fields.https://resolver.caltech.edu/CaltechTHESIS:10232019-170411829Topics in Grand Unified Theories: i) The Naturalness Problem. ii) Monopoles and Fermion Number Violation
https://resolver.caltech.edu/CaltechTHESIS:10232019-171800698
Year: 1983
DOI: 10.7907/m0cj-7n28
<p>This dissertation consists of two parts. The first part contains a discussion of the 'fine-tuning' and 'naturalness ' problems in grand unified theories. It is argued that, while it is impossible to solve these problems in conventional theories which contain scalars, supersymmetric theories that require no fine tuning can be constructed. In these theories the problem reduces to that of obtaining a light Higgs doublet at the tree level, without any unnatural adjustment of parameters. A realistic supersymmetric grand unified theory that has this feature is constructed. It is based on the gauge group SO(10). Supersymmetry is explicitly broken through terms of dimension two.</p>
<p>The second part is an analysis of the interaction of fermions with a non-Abelian ('t Hooft-Polyakov) monopole. Monopoles are invariably present in grand unified theories, and recent studies with massless isospin half fermions have shown that monopoles catalyse fermion number violation. We show that this phenomenon can be described in simple terms using the language of instanton physics. This description also permits a straightforward extension of previous results to arbitrary fermion representations. The importance of half-integer winding numbers is stressed. An explicit calculation is done in the case of isovector fermions.</p>https://resolver.caltech.edu/CaltechTHESIS:10232019-171800698Yang-Mills Theory in Six-Dimensional Superspace
https://resolver.caltech.edu/CaltechTHESIS:06042014-113206988
Year: 1984
DOI: 10.7907/RP3T-S865
<p>The superspace approach provides a manifestly supersymmetric formulation of supersymmetric theories. For N= 1 supersymmetry one can use either constrained or unconstrained superfields for such a formulation. Only the unconstrained formulation is suitable for quantum calculations. Until now, all interacting N>1 theories have been written using constrained superfields. No solutions of the nonlinear constraint equations were known.</p>
<p>In this work, we first review the superspace approach and its relation to conventional component methods. The difference between constrained and unconstrained formulations is explained, and the origin of the nonlinear constraints in supersymmetric gauge theories is discussed. It is then shown that these nonlinear constraint equations can be solved by transforming them into linear equations. The method is shown to work for N=1 Yang-Mills theory in four dimensions. </p>
<p>N=2 Yang-Mills theory is formulated in constrained form in six-dimensional superspace, which can be dimensionally reduced to four-dimensional N=2 extended superspace. We construct a superfield calculus for six-dimensional superspace, and show that known matter multiplets can be described very simply. Our method for solving constraints is then applied to the constrained N=2 Yang-Mills theory, and we obtain an explicit solution in terms of an unconstrained superfield. The solution of the constraints can easily be expanded in powers of the unconstrained superfield, and a similar expansion of the action is also given. A background-field expansion is provided for any gauge theory in which the constraints can be solved by our methods. Some implications of this for superspace gauge theories are briefly discussed. </p>
https://resolver.caltech.edu/CaltechTHESIS:06042014-113206988Finiteness in Supersymmetric Theories
https://resolver.caltech.edu/CaltechTHESIS:11262018-165108335
Year: 1984
DOI: 10.7907/4t2f-t947
<p>A two loop calculation in the N = 4 supersymmetric Yang Mills theory is performed in various dimensions. The theory is found to be two-loop finite in six dimensions or less, but infinite in seven and nine dimensions. The six-dimensional result can be explained by a formulation of the theory in terms of N = 2 superfields. The divergence in seven dimensions is naively compatible with both N=2 and N=4 superfield power counting rules, but is of a form that cannot be written as an on-shell N=4 superfield integral. The hypothesized N=4 extended superfield formalism therefore either does not exist, or at least has weaker consequences than would have been expected. By analogy, four-dimensional supergravity theories are expected to be infinite at three loops.</p>
<p>Some general issues about the meaning of finiteness in nonrenormalizable theories are discussed. In particular, the use of field redefinitions, the generalization of wavefunction renormalizations to nonrenormalizable theories, and whether counterterms should be used in calculations in "finite" theories are studied. It is shown that theories finite to n loops can have at most simple-pole divergences at n + 1 loops.</p>
<p>A method for simplifying the calculation of infinite parts of Feynman diagrams is developed. Based on the observation that counterterms are local functions, all integrals are reduced to logarithmically divergent ones with no dependence on masses or external momenta. The method is of general use, and is particularly effective for many-point Green functions at more than one loop.</p>https://resolver.caltech.edu/CaltechTHESIS:11262018-165108335A Systematic Study of the Decays of Charmed D Mesons
https://resolver.caltech.edu/CaltechTHESIS:01312019-122402912
Year: 1985
DOI: 10.7907/g0wf-ny80
<p>A large sample of D mesons, produced by the decay of the Ψ(3770) and observed by the Mark III detector at SPEAR, forms the basis for a study of the decays of charmed D<sup>+</sup> and D<sup>0</sup> mesons. Many Cabibbo-allowed and Cabibbo-suppressed decays are observed. When normalized by a new, absolute technique, the branching ratios appear significantly higher than those reported by previous experiments. No evidence is found for specific final states from D<sup>0</sup> decay which are indicative of non-spectator W-exchange diagrams: limits are quoted. Finally, the inclusive semileptonic branching fractions of charged and neutral D mesons are measured by observation of electrons in the recoil from fully reconstructed hadronic D decays of known charm. By neglecting the contribution of Cabibbo-suppressed decays to the total decay widths, the ratio of these branching fractions can be interpreted as the ratio of D<sup>+</sup> and D<sup>0</sup> lifetimes, thus confirming the inequality of lifetimes observed by direct decay length experiments. The observed pattern of hadronic decays appears to favor modification of the spectator model over non-spectator processes as the main source of the lifetime difference.</p>https://resolver.caltech.edu/CaltechTHESIS:01312019-122402912Supergravity Theory from Ten Dimensions
https://resolver.caltech.edu/CaltechTHESIS:01312019-162531115
Year: 1985
DOI: 10.7907/wt9n-gm39
<p>This work is concerned with the study of several ten-dimensional field theories intimately associated with superstring theories, and possibilities for obtaining realistic four-dimensional theories from them.</p>
<p>Three chapters follow the N = 2b supergravity from ten to five, then to four dimensions . First of all, compactifications to five dimensions on various manifolds are studied. Then the entire mass spectrum for the compactification on S<sup>5</sup> is derived using techniques of harmonic analysis on spheres. A particular set of modes corresponds to a gauged maximal super gravity theory in five dimensions; this theory, with Yang-Mills group SO(6), is constructed in detail. By a process similar to analytic continuation, noncompact versions of this theory are also obtained, gauging all the semisimple real forms of SO(6). One particular form, with gauge group SO*(6) ≈ SU(3,1), compactifies to fiat four-dimensional spacetime and offers attractive phenomenological possibilities.</p>
<p>The final chapter is concerned with candidates for effective low-energy theories for N = 1 superstrings with gauge group SO(32) or E<sub>8</sub> x E<sub>8</sub>. These effective theories contain curvature squared terms, and require unusual gravitational interactions to cancel anomalies. The field equations are derived and found to admit compactifications to fiat four dimensional spacetime, with the possibility of accommodating many phenomenological considerations.</p>https://resolver.caltech.edu/CaltechTHESIS:01312019-162531115Dynamical Electromagnetic Fields Near Black Holes and Multipole Moments of Stationary, General Relativistic Systems
https://resolver.caltech.edu/CaltechTHESIS:09012017-090944275
Year: 1985
DOI: 10.7907/xayq-7806
<p>This dissertation contains two works; one of the behavior of dynamical electromagnetic fields in the stationary spacetime generated by a black hole, and the other on the structure of a general stationary vacuum spacetime itself.</p>
<p>The study of electromagnetic field is carried out in terms of the "membrane formalism" for black holes; and it is part of a series of papers with the aim of developing that formalism into a complete, self-consistent description of electromagnetic and gravitational fields in a black hole background. Various model problems are presented as aids in understanding the interactions of electromagnetic fields with a black hole, and special attention is paid to the concept of the "stretched horizon" which is vital for the membrane formalism.</p>
<p>The second work develops a multipole moment formalism for a general stationary system in general relativity. The multipole moments are defined in terms of a general formal series solution of the stationary Einstein equation, in analogy to multipole moments in the Newtonian theory of gravity. These relativistic moments exhibit many desirable properties and are shown to be useful in studying the interactions between a gravitating body and an external gravitational field. A model calculation applying the formalism to a black hole interacting with an external multipole field shows that the interaction can be understood in terms of "elastic moduli" of the black-hole horizon.</p>https://resolver.caltech.edu/CaltechTHESIS:09012017-090944275The Ultraviolet Divergences of Einstein Gravity
https://resolver.caltech.edu/CaltechTHESIS:04052019-155701481
Year: 1986
DOI: 10.7907/zntd-4x91
<p>We discuss a two-loop calculation showing that the S matrix of Einstein's theory of gravity contains nonrenormalizable ultraviolet divergences in four dimension. We discuss the calculation in both background field and normal field theory. We describe a new method for dealing with ghost fields in gauge theories by combining them with suitable extensions of the gauge fields in higher dimensions. We show how using subtracted integrals in the calculation of higher loop graphs simplifies the calculation in the background field method by eliminating the need for "mixed" counterterms. Finally, we make some remarks about the implications of our result for supergravity theories.</p>https://resolver.caltech.edu/CaltechTHESIS:04052019-155701481Interactions of Strings Compactified on Orbifolds
https://resolver.caltech.edu/CaltechTHESIS:08012017-135315454
Year: 1987
DOI: 10.7907/gvyt-8e89
<p>It is very important to understand the process of string compactification before one can extract any reliable phenomenology. We consider an exactly solvable method of string compactification, in which the internal space is an orbifold. We compute various interaction amplitudes and describe how other amplitudes can be calculated.</p>
<p>Multi-valued string variables are handled by formulating the amplitudes on covering spaces where they become single-valued. In the computation of the amplitudes, stretched string intermediate states give rise to expressions that are non-perturbative from the non-linear sigma model point of view.</p>
<p>We also discuss, in the context of Z orbifold, the "blowing up" of the fixed points of an orbifold, to give rise to a Calabi-Yau manifold. The resulting Calabi-Yau manifold is shown to be non-perturbatively stable.</p>https://resolver.caltech.edu/CaltechTHESIS:08012017-135315454Some Aspects of the Quantization of Theories with a Gauge Invariance
https://resolver.caltech.edu/CaltechTHESIS:08042017-154857683
Year: 1987
DOI: 10.7907/hf4w-dw98
<p>We discuss some problems that arise when one tries to quantize a theory that possesses gauge degrees of freedom. First, we identify the Gribov problem that is encountered when the Faddeev-Popov procedure of fixing the gauge is employed to define a perturbation expansion. We propose a modification of the procedure that takes this problem into account. We then apply this method to two-dimensional gauge theories where the exact answer is known. Second, we try to build chiral theories that are consistent in the presence of anomalies, without making use of additional degrees of freedom. We are able to solve the model exactly in two dimensions, arriving at a gauge-invariant theory. We discuss the four-dimensional case and also the application of this method to string theory. In the latter, we obtain a model that lives in arbitrary dimensions. However, we do not compute the spectrum of the model. Third, we investigate the possibility of compactifying the unwanted dimensions of superstrings on a group manifold. We give a complete list of conformally invariant models. We also discuss one-loop modular invariance. We consider both type-II and heterotic superstring theories. Fourth, we discuss quantization of string field theory. We start by presenting the lagrangian approach, to demonstrate the non-uniqueness of the measure in the path-integral. It is fixed by demanding unitarity, which manifests itself in the hamiltonian formulation, studied next.</p>https://resolver.caltech.edu/CaltechTHESIS:08042017-154857683On the BRST Invariance of String Theory
https://resolver.caltech.edu/CaltechETD:etd-01052005-142036
Year: 1988
DOI: 10.7907/MDK4-NY02
<p>Radiative corrections to string scattering amplitude generate, in general, BRST anomalies due to the massless particle tadpole, the on-shell external two-point function singularities, and the intermediate unphysical cut singularities. It is proved that they originate from the boundaries of moduli space. Unitarity, analyticity, and BRST invariance are restored only after we add appropriate local counterterms to the scattering amplitudes. We show that counterterms have physical interpretations as the Fischler-Susskind mechanism, the mass renormalization, and the contact interactions respectively.</p>
https://resolver.caltech.edu/CaltechETD:etd-01052005-142036Topics in Conformal Field Theory
https://resolver.caltech.edu/CaltechTHESIS:03112013-144150219
Year: 1988
DOI: 10.7907/xp2b-x462
<p>In this work two major topics in Conformal Field Theory are discussed. First a detailed investigation of N=2 Superconformal theories is presented. The structure of the representations of the N=2 superconformal algebras is investigated and the character formulae are calculated. The general structure of N=2 superconformal theories is elucidated and the operator algebra of the minimal models is derived. The first minimal system is discussed in more detail. Second, applications of the conformal techniques are studied in the Ashkin-Teller model. The c = 1 as well as the c = ½ critical lines are discussed in detail.</p>
https://resolver.caltech.edu/CaltechTHESIS:03112013-144150219The Singular Mechanics of Particles and Strings
https://resolver.caltech.edu/CaltechTHESIS:01172013-111439406
Year: 1988
DOI: 10.7907/hvjy-be63
<p>The quantum mechanics of singular systems is a topic of considerable importance for all the theories of elementary particle physics in which gauge invariance is a universal attribute. This is especially true for string theories which are gauge theories <i>par excellence</i>.</p>
<p>This thesis begins with a brief exposition of singular Hamiltonian mechanics. This tool is applied principally to manifestly supersymmetric particle and string theories. The Dirac particle and the bosonic particle and string are briefly examined. In particular, a method is shown for quantizing the point superparticle in four and ten dimensions. The two actions proposed for describing the manifestly supersymmetric string are shown to be essentially equivalent. The problems of their quantization are briefly discussed.</p>https://resolver.caltech.edu/CaltechTHESIS:01172013-111439406Effective Lagrangians and Infinity Cancellations for Open String Theories
https://resolver.caltech.edu/CaltechTHESIS:01172013-140801181
Year: 1988
DOI: 10.7907/9vpf-s680
<p>The covariant path integral formalism for theories of open and closed strings is
used to study the first order of string perturbation theory beyond tree level for the
closed-string states, in which the string world sheet has the topology of the disk or the
real projective plane. We find that scattering amplitudes (in flat spacetime) confirm
these surfaces' contribution to the low-energy effective action for the bosonic string
theory, as derived by another method, demanding consistency of string propagation in
background gravitational and dilaton fields (the "sigma model approach"). However,
we are not able to obtain results consistent with this effective action by demanding
that amplitudes in a curved background be finite; this is an unresolved puzzle. Decoupling
of spurious tachyon states from the superstring S-matrix is discussed, and
finiteness of amplitudes for the disk plus projective plane is demonstrated for a large
class of external states, when the gauge group is SO(32).</p>https://resolver.caltech.edu/CaltechTHESIS:01172013-140801181G/H Conformal Field Theory
https://resolver.caltech.edu/CaltechETD:etd-08202008-083708
Year: 1988
DOI: 10.7907/YNEZ-8X17
<p>We show that for every affine Lie algebra G and subalgebra H there exists an exactly solvable two-dimensional conformal field theory, and give a procedure for explicitly determining its correlation functions and partition function given those for the Wess-Zumino-Witten models with symmetry algebras G and H.</p>https://resolver.caltech.edu/CaltechETD:etd-08202008-083708Some Aspects of Open String Field Theories
https://resolver.caltech.edu/CaltechETD:etd-06072007-104420
Year: 1990
DOI: 10.7907/qgks-pd11
<p>The construction of covariant string field theories is an important step toward a deeper understanding of string theories. This thesis discusses the general formulation of bosonic and supersymmetric covariant open string field theories and their second quantization. A particular emphasis is given to the perturbative calculation in the framework of string field theory. The use of string wave functional and the technique of conformal field theory are illustrated by explicit calculations of on- and off-shell string amplitudes. The background independent cubic actions for open strings are described briefly.</p>https://resolver.caltech.edu/CaltechETD:etd-06072007-104420On quantum fluctuations and black holes
https://resolver.caltech.edu/CaltechETD:etd-09112008-135620
Year: 1994
DOI: 10.7907/8jtc-0d19
We explore some exotic phenomena in charged black holes, arising from the second quantization of matter fields or from the first quantization of fundamental strings. Spherically symmetric magnetic black holes admit special modes of electrically charged fermions, known as Callan-Rubakov modes, which can be quantized efficiently. We find that the chargeless sector generates non-thermal quantum radiations from extremal Reissner-NordstrOm black holes, thereby reducing the black hole masses below the familiar classical bound in spite of the vanishing Hawking temperature. On the other hand, the charged sector induces a vacuum energy distribution and the gravitational backreaction thereof, which are particularly pronounced for extremal dilatonic black holes. Implications of these quantum effects are studied in great detail. Also considered is a string-inspired two-dimensional gravity with non-singular charged black holes among its solutions. After a lengthy discussion on the stability of these novel space-times, we speculate on the possibility and implications of nonsingular black holes in full-blown string theories.
https://resolver.caltech.edu/CaltechETD:etd-09112008-135620Branes, Brane Actions and Applications to Field Theory
https://resolver.caltech.edu/CaltechETD:etd-12082006-104418
Year: 2001
DOI: 10.7907/qr6g-tp18
This thesis describes the construction of supersymmetric world-volume actions for various kinds of extended objects that appear in string theory, the so-called p-branes, D-branes and M-branes. We also present an application of branes to computing the spectrum of a conformal field theory in the context of the AdS-CFT correspondence.
https://resolver.caltech.edu/CaltechETD:etd-12082006-104418Brane Models and the Hierarchy Problem
https://resolver.caltech.edu/CaltechTHESIS:06242010-150733171
Year: 2001
DOI: 10.7907/zmfm-yd07
It has been recently proposed that higher-dimensional field theory models in the presence of extended defects ("branes") may play a role in addressing the gauge hierarchy problem. In this thesis we consider several aspects of such field theories. First we perform the Kaluza-Klein reduction of a bulk scalar field propagating in the scenario of Randall and Sundrum, which consists of a region of five-dimensional anti-deSitter space bounded by two three-branes. We then propose a simple mechanism, based on the dynamics of a bulk scalar field, for stabilizing the modulus field (the "radion") corresponding to the size of the compact dimension in the Randall-Sundrum scenario. Some implications of this stabilization mechanism for low-energy phenomenology are described. Next, we investigate the one-loop quantum corrections to the radion effective potential. We show that for large brane separation, the quantum effects are power suppressed and therefore have a negligible effect on the bulk dynamics once a classical stabilization mechanism is in place. Finally, we study the ultraviolet divergence structure of field theory in the presence of branes and find that brane-localized divergences arise both at the classical and quantum level. We show how to interpret the classical divergences by the usual regularization and renormalization procedure of quantum field theory.https://resolver.caltech.edu/CaltechTHESIS:06242010-150733171D-Branes in Anti-de-Sitter Space
https://resolver.caltech.edu/CaltechETD:etd-06022003-200011
Year: 2003
DOI: 10.7907/ZE9Y-RP78
<p>We investigate the role of Dp-branes, which are p+1 dimensional membranes where open strings end, in two different types of anti-de-Sitter backgrounds: AdS₃ x S₃ x M⁴ and AdS₅ x S⁵, where M⁴ is a compact four-dimensional manifold such as the four-torus T4 or the K3 surface.</p>
<p>In the spirit of the AdS/CFT correspondence, D-brane physics on an anti-de-Sitter space should be captured by a dual conformal field theory defined on the boundary of AdS. Recently, Karch and Randall and DeWolfe, Freedman and Ooguri proposed in that the presence of a single D5-brane in AdS₅ x S⁵ is dual to a defect conformal field theory in which the usual N=4 bulk SYM theory is coupled to a 2+1 dimensional conformal defect field theory. Extending their result, we take the Penrose limit of a single D5-brane embedded in AdS₅ x S⁵ and propose a correspondence between open string states ending on the D5-brane and gauge-invariant operators living on the dual defect conformal field theory. Furthermore, we check this proposal by verifying that the anomalous dimension of the gauge theory operators matches the light-cone Hamiltonian of open strings ending on the D5-brane.</p>
<p>Maldacena has proposed that type IIB string theory compactified on AdS₃ x S₃ x M⁴ is dual to a 1+1 conformal field theory defined on the conformal boundary of AdS₃. In this thesis, we restrict our attention to the study of a D-brane embedded in AdS₃ x S₃ x M⁴ backgrounds and leave the explicit construction of the AdS/CFT correspondence of this setup for future work by others. First, we investigate the spectrum of open strings on AdS₂ branes in AdS₃ in an NS-NS background using the SL(2,R) WZW model. Then, we construct boundary states for the AdS₂ branes in the Euclideanized AdS₃ background and compute the one-loop free energy of open strings stretched between the branes.</p>https://resolver.caltech.edu/CaltechETD:etd-06022003-200011String/Gauge Duality and Penrose Limit
https://resolver.caltech.edu/CaltechETD:etd-05152003-134850
Year: 2003
DOI: 10.7907/4S7W-2F30
<p>Berenstein, Maldacena, and Nastase have recently discovered a particular limit of AdS/CFT correspondence where string theory in a plane wave background is dual to a sector of $mathcal N =4 SYM in a double scaling limit. It is based on the observation that a plane wave background can be obtained by taking Penrose limit of Anti de Sitter background. The corresponding gauge theory limit is identified via AdS/CFT dictionary. This proposal is especially exciting because string worldsheet theory in a plane wave background is exactly solvable, thereby opening a possibility that one can go beyond supergravity approximation. In the absence of string interactions, the duality made a remarkable prediction for anomalous dimension of gauge theory operators from exact free string spectrum, which was soon verified.</p>
<p>In this thesis, we attempt to extend the duality to the interacting theory level. We propose that the correct holographic recipe is to identify the full string field theory Hamiltonian with the dilatation operator of gauge theory. In practice, we must find an identification map between string theory and gauge theory Hilbert spaces and evaluate matrix elements of the two operators accordingly. The requirement that the inner product should be preserved determines a unique identification map assuming that it is hermitian. We show that transition amplitudes of string field theory agree with matrix elements of dilatation operator under this preferred identification for states with two different impurities. We later extend it to states with arbitrary impurities. In doing so, we find a diagrammatic correspondence between string field theory and gauge theory Feynman diagrams thereby providing direct handles on the duality. Our proposal is universal in the sense that it is applicable to any interaction type such as the open-closed interaction, and to all orders in g₂ and λ'. Hopefully, this thesis will be a key step towards proving the novel duality and a beginning of an exciting journey to the stringy regime of string/gauge duality.</p>https://resolver.caltech.edu/CaltechETD:etd-05152003-134850RG-Flows, AdS/CFT Correspondence and Stability of Non-Dilatonic Branes
https://resolver.caltech.edu/CaltechETD:etd-04272005-130936
Year: 2004
DOI: 10.7907/DQKG-HY63
The possibility of having multiple renormalization group (RG) flows (one of which is supersymmetric) between two fixed points is investigated in the context of anti de Sitter / conformal field theory (AdS/CFT) correspondence. An analysis of a toy-model potential suggests that such flows are likely to exist. Superpotential methods are used in the context of finite temperature AdS/CFT to derive a black brane solution which approximates various finite temperature RG-flows in AdS/CFT near the horizon. This solution is also used in formulating a notion of univerality classes of instabilities of black braves. Instabilities of D3, M2 and M5-branes are investigated numerically, and the results confirm the predictions of the proposal of universality classes.https://resolver.caltech.edu/CaltechETD:etd-04272005-130936Monopole Operators and Mirror Symmetry in Three-Dimensional Gauge Theories
https://resolver.caltech.edu/CaltechETD:etd-04062004-015855
Year: 2004
DOI: 10.7907/5AP4-X614
<p>Many gauge theories in three dimensions flow to interacting conformal field theories in the infrared. We define a new class of local operators in these conformal field theories that are not polynomial in the fundamental fields and create topological disorder. They can be regarded as higher-dimensional analogs of twist and winding-state operators in free 2-D CFTs. We call them monopole operators for reasons explained in the text. The importance of monopole operators is that in the Higgs phase, they create Abrikosov-Nielsen-Olesen vortices. We study properties of these operators in three-dimensional gauge theories using large N_f expansion. For non-supersymmetric gauge theories we show that monopole operators belong to representations of the conformal group whose primaries have dimension of order N_f. We demonstrate that these monopole operators transform non-trivially under the flavor symmetry group.</p>
<p>We also consider topology-changing operators in the infrared limits of N=2 and N=4 supersymmetric QED as well as N=4 SU(2) gauge theory in three dimensions. Using large N_f expansion and operator-state isomorphism of the resulting superconformal field theories, we construct monopole operators that are primaries of short representation of the superconformal algebra and compute their charges under the global symmetries. Predictions of three-dimensional mirror symmetry for the quantum numbers of these monopole operators are verified. Furthermore, we argue that some of our large-N_f results are exact. This implies, in particular, that certain monopole operators in N=4 3-D SQED with N_f=1 are free fields. This amounts to a proof of 3-D mirror symmetry in these special cases.</p>https://resolver.caltech.edu/CaltechETD:etd-04062004-015855D-Brane Actions and N=2 Supergravity Solutions
https://resolver.caltech.edu/CaltechETD:etd-06022004-125935
Year: 2004
DOI: 10.7907/WSR1-2S04
<p>Among the most remarkable recent developments in string theory are the AdS/CFT duality, as proposed by Maldacena, and the emergence of noncommutative geometry. It has been known for some time that for a system of almost coincident D-branes the transverse displacements that represent the collective coordinates of the system become matrix-valued transforming in the adjoint representation of U(N). From a geometrical point of view this is rather surprising but, as we will see in Chapter 2, it is closely related to the noncommutative descriptions of D-branes.</p>
<p>A consequence of the collective coordinates becoming matrix-valued is the appearance of a dielectric effect in which D-branes can become polarized into higher-dimensional fuzzy D-branes. This last aspect has inspired Polchinski and Strassler to find a nonsingular string dual of a confining four-dimensional gauge theory. The nonsingular geometry is sourced by an extended brane arising from Myers' dielectric effect. Following the spirit of the Polchinski-Strassler paper, we find N = 2 supergravity solutions with polarized branes and a field-theory dual. In our case we are able to present exact supergravity solutions by using M-theory reductions to type IIA supergravity.</p>https://resolver.caltech.edu/CaltechETD:etd-06022004-125935Testing Gauge/Gravity Duality: The Eleven-Dimensional PP-Wave
https://resolver.caltech.edu/CaltechETD:etd-05252004-230238
Year: 2004
DOI: 10.7907/0JV2-RT78
The gauge/gravity duality in the interaction between M theory objects has taught us a lot about quantum gravity. The eleven-dimensional PP-wave background provides a new arena for exploring this duality beyond flat and almost flat, i.e., weakly curved, backgrounds. In this thesis we discuss the gauge theories that describe the dynamics of interacting M theory objects, the supergravity calculations that capture these dynamics, the comparison of the two sides, and various objects (such as gravitons and membranes) in the eleven-dimensional PP-wave background. We only consider the one-loop gauge theory and linearized supergravity approximations.
https://resolver.caltech.edu/CaltechETD:etd-05252004-230238The Near-Penrose Limit of AdS/CFT
https://resolver.caltech.edu/CaltechETD:etd-05252005-175001
Year: 2005
DOI: 10.7907/EHS6-QF38
The conjectured duality between type IIB string theory on AdS5 x S5 and N = 4 SU(Nc) super Yang-Mills theory in four dimensions simplifies in the Penrose limit or, in other words, when the string's angular momentum is large. As the string action in this limit is solvable, it is possible to go beyond the supergravity approximation and compare exact string energies with the anomalous dimensions of a sector of large R-charge operators. This equivalence should of course extend to the full AdS5 x S5 space and to operators of finite R-charge. We take some modest steps in this direction by expanding the full string action in inverse powers of the angular momentum and finding the first order perturbative corrections to the energy spectrum. These corrections reproduce the gauge theory anomalous dimensions for a range of different operators to two-loops in the 't Hooft parameter but disagree at three-loops. Furthermore, these near-plane wave results are useful in studying the recently discovered integrability in this AdS/CFT system and can be used to motivate the form of quantum string scattering matrices.https://resolver.caltech.edu/CaltechETD:etd-05252005-175001Large N Dualities in Topological String Theory
https://resolver.caltech.edu/CaltechETD:etd-05232005-184326
Year: 2005
DOI: 10.7907/YJVK-6M26
<p>We investigate the phenomenon of large N duality in topological string theory from three different perspectives: worldsheets, matrix models, and melting crystals.</p>
<p>In the first part, we utilize the technique of mirror symmetry to generalize the worldsheet derivation of the duality, originally given by Ooguri and Vafa for the A-model on the conifold, to the A-model on more general geometries. We also explain how the Landau-Ginzburg models can be used to perform the worldsheet derivation of the B-model large N dualities.</p>
<p>In the second part, we consider a class of A-model large N dualities where the open string theory reduces through the Chern-Simons theory on a lens space to a matrix model. We compute and compare the matrix model spectral curve and the Calabi-Yau geometry mirror to the closed string geometry, confirming the predictions of the duality.</p>
<p>Finally in the third part, we propose a crystal model that describes the A-model on the resolved conifold. This is a generalization of the crystal for C³. We also consider a novel unitary matrix model for the Chern-Simons theory on the three-sphere and show how the crystal model for the resolved conifold is derived from the matrix model. Certain non-compact D-branes are naturally incorporated into the crystal and the matrix model.</p>https://resolver.caltech.edu/CaltechETD:etd-05232005-184326Topological Sigma Models and Generalized Geometries
https://resolver.caltech.edu/CaltechETD:etd-05262005-154458
Year: 2005
DOI: 10.7907/RMHE-4185
We study the relation between topological sigma models and generalized geometries. The existence conditions for the most general type of topological sigma models obtained from twisting the N=(2,2) supersymmetric sigma model are investigated, and are found to be related to twisted generalized Calabi-Yau structures. The properties of these topological sigma models are analyzed in detail. The observables are shown to be described by the cohomology of a Lie algebroid, which is intrinsically associated with the twisted generalized Calabi-Yau structure. The Frobenius structure on the space of states and the effects of instantons are analyzed. We also study D-branes in these topological sigma models, and demonstrate that they also admit descriptions in terms of generalized geometries.https://resolver.caltech.edu/CaltechETD:etd-05262005-154458Heavy Pentaquarks in the Diquark Model and the Large Nc Expansion
https://resolver.caltech.edu/CaltechETD:etd-05232005-174621
Year: 2005
DOI: 10.7907/6812-4G64
<p>Recent experimental evidence for the Θ⁺(1540) has given rise to much theoretical interest in exotic baryons. The Θ⁺ is a baryon that has strangeness S=+1, meaning that it contains an anti-strange quark. Thus it cannot be constructed from three quarks, unlike all other known baryons; it needs at least an extra quark-antiquark pair. It is usually modeled as a pentaquark state in the 10 bar representation of flavor SU(3), with flavor content s̅uudd.</p>
<p>This thesis considers possible heavy pentaquarks, in which the antiquark is charmed or bottom rather than strange. In the context of the diquark model of Jaffe and Wilczek, it is argued that negative-parity pentaquarks of this type may be lighter than their positive-parity counterparts, and hence are likely to be stable against strong decay. Estimates are made for their masses, and their weak decays are discussed. Isospin relations are found between the decay rates for different possible decay channels.</p>
<p>Negative-parity heavy pentaquarks are also considered in a less model-dependent way, in the context of a 1/Nc expansion, where Nc is the number of colors. Heavy quark effective theory is also employed. Mass relations are found between the mass splittings of heavy pentaquarks and those of nonexotic baryons, and SU(3)-breaking corrections to these relations are computed. The results could be helpful in interpreting experimental data if heavy pentaquarks are observed.</p>https://resolver.caltech.edu/CaltechETD:etd-05232005-174621Probing Physics and the Standard Model and Beyond with Electroweak Baryogenesis and Effective Theories of the Strong Interactions
https://resolver.caltech.edu/CaltechETD:etd-05272005-162229
Year: 2005
DOI: 10.7907/GJPE-HN05
<p>We address in this thesis two primary questions aimed at improving our ability to calculate reliably in the Standard Model of particle physics and probing possible new particles which may exist beyond it.</p>
<p>First, we embark on an attempt to account for the abundance of matter in the present Universe if earlier in its history matter and antimatter were equally abundant. We explore whether baryogenesis at the electroweak phase transition could successfully account for the observed density of baryons in the Universe, using the closed-time-path (CTP) formalism of quantum field theory to calculate the buildup and relaxation of particle densities during the phase transition. For our model of the new particles and sources of CP violation necessary to account for the baryon asymmetry of the Universe, we adopt the Minimal Supersymmetric Extension of the Standard Model (MSSM). We look for regions of the parameter space in the MSSM that could give rise to sufficiently large baryon asymmetry without violating constraints on these parameters from existing experiments, in particular, constraints on masses of Higgs and supersymmetric particles from accelerator searches and precision electroweak tests, and on CP-violating parameters of the MSSM from searches for electric dipole moments of elementary particles.</p>
<p>Next, we explore how to get around our ignorance of the dynamics of strongly interacting particles in the nonperturbative regime of Quantum Chromodynamics (QCD) by the clever use of effective field theories. Two applications are explored: the decay of Z bosons to hadronic jets using soft-collinear effective theory (SCET) and the radiative decays of quarkonia to light hadrons using SCET and non-relativistic QCD (NRQCD). These tools facilitate the proof of factorization of decay rates into perturbatively-calculable and nonperturbative parts. Universality of the latter among different observables provides predictive power even in our ignorance of the details of the nonperturbative physics.</p>https://resolver.caltech.edu/CaltechETD:etd-05272005-162229Gauge Theory and Supergravity Duality in the PP-Wave Background
https://resolver.caltech.edu/CaltechETD:etd-05262005-151056
Year: 2005
DOI: 10.7907/8QS9-Q326
We test the matrix theory conjecture in the pp-wave by studying two-body interactions between gravitons and membranes. We compute the one-loop effective potential of matrix theory and compare it to the light cone Lagrangian of linearized supergravity. We have exact agreement in the absence of M-momentum transfer. We also find the effective potential that smoothly interpolates between the spherical membrane result and the graviton result. We also collect here partial results from our investigation of interactions with M-momentum transfer.https://resolver.caltech.edu/CaltechETD:etd-05262005-151056Superstring Holography and Integrability in AdS₅ x S⁵
https://resolver.caltech.edu/CaltechETD:etd-05042005-144547
Year: 2005
DOI: 10.7907/QD85-9603
The AdS/CFT correspondence provides a rich testing ground for many important topics in theoretical physics. The earliest and most striking example of the correspondence is the conjectured duality between the energy spectrum of type IIB superstring theory on AdS₅ x S⁵ and the operator anomalous dimensions of N=4 supersymmetric Yang-Mills theory in four dimensions. While there is a substantial amount of evidence in support of this conjecture, direct tests have been elusive. The difficulty of quantizing superstring theory in a curved Ramond-Ramond background is compounded by the problem of computing anomalous dimensions for non-BPS operators in the strongly coupled regime of the gauge theory. The former problem can be circumvented to some extent by taking a Penrose limit of AdS₅ x S⁵, reducing the background to that of a pp-wave (where the string theory is soluble). A corresponding limit of the gauge theory was discovered by Berenstein, Maldacena and Nastase, who obtained successful agreement between a class of operator dimensions in this limit and corresponding string energies in the Penrose limit. In this dissertation we present a body of work based largely on the introduction of worldsheet interaction corrections to the free pp-wave string theory by lifting the Penrose limit of AdS₅ x S⁵. This provides a new class of rigorous tests of AdS/CFT that probe a truly quantum realm of the string theory. By studying the correspondence in greater detail, we stand to learn not only about how the duality is realized on a more microscopic level, but how Yang-Mills theories behave at strong coupling. The methods presented here will hopefully contribute to the realization of these important goals.https://resolver.caltech.edu/CaltechETD:etd-05042005-144547Topics in Heavy Particle Effective Theories
https://resolver.caltech.edu/CaltechETD:etd-05262006-125115
Year: 2006
DOI: 10.7907/2SCF-KR56
<p>This thesis gives several applications of effective field theory to processes involving heavy particles. The first is a standard application of heavy quark effective theory to exclusive B decays. It involves two sum rules giving constraints on the curvature of the B→D Isgur-Wise function. This thesis calculates order alpha corrections to these constraints, increasing the accuracy of the resultant constraints on the physical form factors.</p>
<p>The second application involves matching SCETI onto SCET<sub>II</sub> at one loop. Keeping the external fermions off their mass shell does not regulate all IR divergences in both theories. The work described here gives a new prescription to regulate infrared divergences in SCET. Using this regulator, we show that soft and collinear modes in SCET<sub>II</sub> are sufficient to reproduce all the infrared divergences of SCET<sub>I</sub>. We explain the relationship between IR regulators and an additional mode proposed for SCET<sub>II</sub>.</p>
<p>Next we consider top production at large energies. The production process is characterized by three disparate energy scales: the center-of-mass energy (E), the mass (m), and the decay width (Gamma). At the scale E we match onto massive soft-collinear effective theory (SCET). The SCET current is run from E to m, thereby summing Sudakov logarithms of the form log<sup>n</sup>(m/E), where n=2,1. At the scale m, the top quark mass is integrated out by matching SCET jet functions onto a boosted version of heavy quark effective theory (bHQET). The jet functions in bHQET are then run from m to Gamma, summing powers of single logarithms of the ratio m/Gamma.</p>
<p>Under certain assumptions factorization formulas can be derived for differential distributions in processes involving highly energetic jets, such as jet energy distributions. As a final topic, we show how to test these assumptions using semileptonic or radiative decays of heavy mesons, by relating the jet P⁺ distribution derived under these assumptions to other differential distributions in these decays, which are better understood.</p>https://resolver.caltech.edu/CaltechETD:etd-05262006-125115On Quantum Interacting Embedded Geometrical Objects of Various Dimensions
https://resolver.caltech.edu/CaltechETD:etd-06072006-174745
Year: 2006
DOI: 10.7907/1VN2-VZ71
Modern string theory naturally gives rise to an assortment of dynamical geometrical objects of various dimensions (collectively referred to as "branes") embedded into spacetime. The aim of this thesis is to present a series of results (of varying novelty and rigor) pertinent to dynamics of the low-dimensional geometrical objects of this kind. The processes considered are the D0-brane recoil and annihilation, "local recoil" of D1-branes (which is a peculiar effect manifested by one-dimensional topological defects in response to an impact, and closely related to soliton recoil), and D- and F-string loop mixing. Apart from the practical relevance within the formalism of string theory, such considerations are worthwhile in that the quantum dynamics of the geometrical objects involved is complex enough to be interesting, yet simple enough to be tractable. Furthermore, some of the results derived here within the string theory formalism may give valuable insights into the dynamics of low-dimensional field-theoretical topological defects.https://resolver.caltech.edu/CaltechETD:etd-06072006-174745Constraints on Physics Beyond the Standard Model and its Observable Effects
https://resolver.caltech.edu/CaltechETD:etd-05282007-034337
Year: 2007
DOI: 10.7907/KSBC-RD46
<p>In this work, we describe three analyses, all of which involve physics beyond the Standard Model. The first two discussed here are closely related; they use effective operator analyses to constrain the contributions of physics beyond the SM to observable processes. The third project involves the investigations of a particular extra-dimensions model which addresses the cosmological constant problem.</p>
<p>The first project which we will discuss uses the scale of neutrino mass to place model-independent constraints on the coefficients of the chirality-changing terms in the muon decay Lagrangian. We list all of the dimension-six effective operators which contribute to muon decay and Dirac mass for the neutrino. We then calculate the one-loop contributions that each of these operators makes to neutrino mass. Taking a generic element of the neutrino mass matrix to be of order ~ 1 eV, we derive limits on the contributions of these operators to the muon Michel parameters which are approximately four orders of magnitude more stringent than the current experimental results, and well below near-future experimental sensitivity. We also find two chirality-changing operators, which, due to their flavor structure, are unconstrained by neutrino mass yet contribute to muon decay. However, as these two operators differ from those constrained by neutrino mass only by their flavor indices, we naively expect their contributions to also be small; if their effects instead turn out to be observable, this may be an indication of beyond-the-Standard-Model physics with an interesting flavor structure.</p>
<p>In the second analysis, we again perform an effective operator analysis, this time applied to Higgs production at a linear collider. Here we include all dimension-six operators containing fermions which contribute to Higgs production. We again include operators that contain right-handed Dirac neutrinos. We obtain limits on these operators from electroweak precision observables, the scale of neutrino mass, and limits on neutrino magnetic moments, and use these limits to constrain the contributions of these operators to the Higgs production cross-section. Although we find that all operators containing right-handed neutrinos contribute negligibly to Higgs production, we do find three operators containing only SM fields which could have observable contributions at an e⁺e⁻ linear collider.</p>
<p>Lastly, we discuss the characteristics of a particular extra-dimensions model originally proposed by Carroll and Guica [54]. This model has two extra dimensions compactified into a sphere, a bulk magnetic field, and a bulk cosmological constant. In this model, the cosmological constant seen by a four-dimensional observer can be set to zero by fine-tuning the bulk magnetic field against the bulk cosmological constant. If branes with a tension are added at each of the poles of the two-sphere, solutions with zero four-dimensional cosmological constant are still possible, but the compactified dimensions must acquire a deficit angle which depends on the brane tension. However, the brane tension does not affect the fine-tuning relationship between the bulk cosmological constant and the bulk magnetic field. This feature led to the hope that, after this fine-tuning, the model might self-tune, keeping the four-dimensional cosmological constant zero regardless of what happens to the brane tension by adjusting the deficit angle. We speculated that this self-tuning property would imply a massless scalar mode in the perturbed Einstein's equations; as there exist very stringent limits on scalar-tensor theories of gravity, a massless scalar mode would make this model incompatible with observation. We conducted a search for such modes, and found none which satisfied the boundary conditions. This finding led us to speculate that this model does not, in fact, have a self-tuning property.</p>https://resolver.caltech.edu/CaltechETD:etd-05282007-034337Aspects of Topological String Theory
https://resolver.caltech.edu/CaltechETD:etd-05272008-225257
Year: 2008
DOI: 10.7907/X29T-G794
Two aspects of the topological string and its applications are considered in this thesis. Firstly, non-perturbative contributions to the OSV conjecture relating four-dimensional extremal black holes and the closed topological string partition function are studied. A new technique is formulated for encapsulating these contributions for the case of a Calabi-Yau manifold constructed by fibering two line bundle over a torus, with the unexpected property that the resulting non-perturbative completion of the topological string partition function is such that the black hole partition function is equal to a product of a chiral and an anti-chiral function. This new approach is considered both in the context of the requirement of background independence for the topological string, and for more general Calabi-Yau manifolds. Secondly, this thesis provides a microscopic derivation of the open topological string holomorphic anomaly equations proposed by Walcher in arXiv:0705.4098 under the assumption that open string moduli do not contribute. In doing so, however, new anomalies are found for compact Calabi-Yau manifolds when the disk one-point functions (string to boundary amplitudes) are non-zero. These new anomalies introduce coupling to wrong moduli (complex structure moduli in A-model and Kahler moduli in B-model), and spoil the recursive structure of the holomorphic anomaly equations. For vanishing disk one-point functions, the open string holomorphic anomaly equations can be integrated to solve for amplitudes recursively, using a Feynman diagram approach, for which a proof is presented.https://resolver.caltech.edu/CaltechETD:etd-05272008-225257Topics in Supersymmetry Breaking and Gauge/Gravity Dualities
https://resolver.caltech.edu/CaltechTHESIS:05042010-150716614
Year: 2010
DOI: 10.7907/9F6Q-ZT22
<p>The thesis covers two topics in string theory and quantum field theory. First, we realize metastable vacua in various supersymmetric gauge theories. Specifically, we consider the Coulomb branch of any N = 2 supersymmetric gauge theory, and perturb it by a superpotential and engineer a metastable vacuum at a point. We also study its relation to Kahler normal coordinates and Fayet-Iliopoulos terms. Having studied the metastable construction, we apply this to general gauge mediation. We show how to compute the current correlators when the hidden sector is strongly coupled in specific examples.</p>
<p>Next, we consider gauge/gravity dualities. We apply dualities to the investigation of various strongly coupled field theories. In one example, we construct M-theory supergravity solutions with the nonrelativistic Schroedinger symmetry starting from the warped AdS_5 metric with N = 1 supersymmetry. We impose that the lightlike direction is compact by making it a nontrivial U(1) bundle over the compact space. In another example, we show that, in a gravity theory with a Chern-Simons coupling, the Reissner-Nordstrom black hole in anti-de Sitter space is unstable depending on the value of the Chern-Simons coupling. The analysis suggests that the final configuration is likely to be a spatially modulated phase.</p>https://resolver.caltech.edu/CaltechTHESIS:05042010-150716614Topics in Topological and Holomorphic Quantum Field Theory
https://resolver.caltech.edu/CaltechTHESIS:06012010-010858409
Year: 2010
DOI: 10.7907/QPRX-0V43
<p>We investigate topological quantum field theories (TQFTs) in two, three, and four dimensions, as well as holomorphic quantum field theories (HQFTs) in four dimensions. After a brief overview of the two-dimensional (gauged) A and B models and the corresponding the category of branes, we construct analogous three-dimensional (gauged) A and B models and discuss the two-category of boundary conditions. Compactification allows us to identify the category of line operators in the three-dimensional A and B models with the category of branes in the corresponding two-dimensional A and B models. Furthermore, we use compactification to identify the two-category of surface operators in the four-dimensional GL theory at t = 1 and t = i with the two-category of boundary conditions in the corresponding three-dimensional A and B model, respectively.</p>
<p>We construct a four-dimensional HQFT related to N = 1 supersymmetric quantum chromodynamics (SQCD) with gauge group SU(2) and two flavors, as well as a four-dimensional HQFT related to the Seiberg dual chiral model. On closed Kahler surfaces with h<sup>(2,0)</sup> > 0, we show that the correlation functions of holomorphic SQCD formally compute certain Donaldson invariants. For simply-connected elliptic surfaces (and their blow-ups), we show that the corresponding correlation functions in the holomorphic chiral model explicitly compute these Donaldson invariants.</p>https://resolver.caltech.edu/CaltechTHESIS:06012010-010858409Refined BPS Invariants, Chern-Simons Theory, and the Quantum Dilogarithm
https://resolver.caltech.edu/CaltechTHESIS:05142010-131147918
Year: 2010-06-11
DOI: 10.7907/Q6WF-D678
In this thesis, we consider two main subjects: the refined BPS invariants of Calabi-Yau threefolds, and three-dimensional Chern-Simons theory with complex gauge group. We study the wall-crossing behavior of refined BPS invariants using a variety of techniques, including a four-dimensional supergravity analysis, statistical-mechanical melting crystal models, and relations to new mathematical invariants. We conjecture an equivalence between refined invariants and the motivic Donaldson-Thomas invariants of Kontsevich and Soibelman. We then consider perturbative Chern-Simons theory with complex gauge group, combining traditional and novel approaches to the theory (including a new state integral model) to obtain exact results for perturbative partition functions. We thus obtain a new class of topological invariants, which are not of finite type, defined in the background of genuinely nonabelian flat connections. The two main topics, BPS invariants and Chern-Simons theory, are connected at both a formal and (we believe) deeper conceptual level by the striking central role that the quantum dilogarithm function plays in each.https://resolver.caltech.edu/CaltechTHESIS:05142010-131147918Integrability of N = 6 Chern-Simons theory
https://resolver.caltech.edu/CaltechTHESIS:05122011-105136289
Year: 2011
DOI: 10.7907/QDSM-8448
In 2008, Aharony, Bergman, Jafferis, and Maldacena (ABJM) discovered a three-dimensional Chern-Simons theory with N = 6 supersymmetry and conjectured that in a certain limit, this theory is dual to type IIA string theory on AdS4xCP3. Since then, a great deal of evidence has been accumulated which suggests that the ABJM theory is integrable in the planar limit. Integrability is a very useful property that allows many physical observables, such as anomalous dimensions and scattering amplitudes, to be computed efficiently. In the first half of this thesis, we will explain how to use integrabilty to compute the anomalous dimensions of long, single-trace operators in the ABJM theory. In particular, we will describe how to compute them at weak coupling using a Bethe Ansatz, and how to compute them at strong coupling using string theory. The latter approach involves using algebraic curve and world-sheet techniques to compute the energies of string states dual to gauge theory operators. In the second half of this thesis, we will discuss integrability from the point of view of on-shell scattering amplitudes in the ABJM theory. In particular, we will describe how to parameterize the amplitudes in terms of supertwistors and how to relate higher-point tree-level amplitudes to lower-point tree-level amplitudes using a recursion relation. We will also explain how this recursion relation can be used to show that all tree-level amplitudes of the ABJM theory are invariant under dual superconformal symmetry. This symmetry is hidden from the point of the action and implies that the theory has Yangian symmetry, which is a key feature of integrability. This thesis is mainly based on the material in [94], [76], and [77].https://resolver.caltech.edu/CaltechTHESIS:05122011-105136289Measurement of Multi-jet Production Cross Section at a Center-of-Mass Energy of 7 TeV at the Large Hadron Collider with the ATLAS Detector
https://resolver.caltech.edu/CaltechTHESIS:05162011-094146813
Year: 2011
DOI: 10.7907/9GWA-6441
Inclusive multi-jet production is studied using proton-proton collisions at a center-of-mass energy of 7 TeV. The data sample corresponds to an integrated luminosity of 2.43 pb<sup>-1</sup>, and uses a subset of the data collected by the ATLAS detector in 2010. Measurements of multi-jet production cross sections with up to six jets are presented and compared to both leading-order predictions enhanced by a parton shower and next-to-leading-order calculations. Generally, agreement is found between data and leading-order and next-to-leading-order predictions. Regions of phase space or observables in which pure parton-shower simulations differ from the measurements are well described by leading-order calculations that combine matrix-element calculations with several outgoing partons in the final state to parton-shower simulations. Measurements compared to next-to-leading-order calculations are shown to be sensitive to the value of the strong coupling constant. https://resolver.caltech.edu/CaltechTHESIS:05162011-094146813Superconformal Chern-Simons Theories and Their String Theory Duals
https://resolver.caltech.edu/CaltechTHESIS:05242011-235017396
Year: 2011
DOI: 10.7907/2D9D-1876
<p>In this thesis, we consider two aspects of the conjectured gauge theory/string theory correspondence between three-dimensional maximal supersymmetric conformal field theories, which describe the world-volume theory of multiple M2-branes in flat space, and M-theory on AdS<sub>4</sub> x S<sup>7</sup>.</p>
<p>First we study three classes of N = 6,8 superconformal Chern-Simons theories that are related to the gauge theory side of the correspondence: the Bagger-Lambert (BL) theories based on 3-algebras, the Lorentzian signature 3-algebra theories, and the Aharony-Bergman-Jafferis-Maldacena (ABJM) theories. We verify the superconformal symmetry of the BL theory, prove that it is parity conserving and conjecture the (by now proven) uniqueness of its SO(4) realization. We then consider the Lorentzian signature 3-algebra theories and show that although the ghosts can be removed to ensure unitarity by gauging certain global symmetries, the resulting theories spontaneously break the conformal symmetry and reduce to maximally supersymmetric three-dimensional Yang-Mills theories. After this, we recast the ABJM theory in a form for which the SU(4) R-symmetry of the action is manifest; then we use this form to verify in complete detail the OSp(6|4) superconformal symmetry of the theory and to express the scalar potential as a sum of squares.</p>
<p>Next, we study the one-loop correction to the energy of a point-particle and circular string solutions to type IIA string theory on AdS<sub>4</sub> x CP<sup>3</sup>. We compute the spectrum of fluctuations for each of these solutions using two techniques, known as the algebraic curve approach and the world-sheet approach. We propose a new prescription for computing the one-loop corrections that gives well-defined results and agrees with the predictions of the all-loop Bethe ansatz for our point-particle and circular string solutions as well as for previous folded-spinning string solutions.</p>https://resolver.caltech.edu/CaltechTHESIS:05242011-2350173964d/2d Correspondence: Instantons and W-Algebras
https://resolver.caltech.edu/CaltechTHESIS:05302012-170816705
Year: 2012
DOI: 10.7907/WP20-DX98
<p>In this thesis, we study the 4d/2d correspondence of Alday-Gaiotto-Tachikawa, which relates the class of 4-dimensional N=2 gauge theories (theories of class S) to a 2-dimensional conformal field theory. The 4d gauge theories are obtained by compactifying 6-dimensional N=(2, 0) theory of type A, D, E on a Riemann surface C. On the 2-dimensional side, we have Toda theory on the surface C with W-algebra symmetry, which is an extension of the Virasoro symmetry. In particular, the instanton partition function of the 4d gauge theory is reproduced by a conformal/chiral block of Virasoro/W-algebra. We develop techniques to compute the partition functions on 4d and 2d sides, for various gauge groups and matter fields.</p>
<p>We generalize the Alday-Gaiotto-Tachikawa 4d/2d correspondence to various cases. First, we study N=2 pure Yang-Mills theory with arbitrary gauge groups, including the exceptional groups. We explicitly construct the corresponding W-algebra currents, and confirm the correspondence holds at 1-instanton level. Second, we study the conformal quiver theory with Sp(1)-SO(4) gauge group. Finally, we study Sicilian gauge theories with trifundamental half-hypermultiplets. We also find that the conformal theories with Sp(1) gauge group and SU(2) gauge group have different instanton partition functions in terms of bare gauge couplings. We show this is an artifact of the renormalization scheme, by explicitly constructing a map between the bare couplings and studying its geometrical interpretations. This demonstrates the scheme independence of renormalization at the non-perturbative level.</p> https://resolver.caltech.edu/CaltechTHESIS:05302012-170816705Localization of Gauge Theories on the Three-Sphere
https://resolver.caltech.edu/CaltechTHESIS:05312012-204458381
Year: 2012
DOI: 10.7907/8AMG-0B70
<p>We describe the application of localization techniques to the path integral for supersymmetric gauge theories in three dimensions. The localization procedure reduces the computation of the expectation value of BPS observables to a calculation in a matrix model. We describe the ingredients of this model for a general quiver gauge theory and the incorporation of supersymmetric deformations and observables.</p>
<p>We use the matrix model expressions to test several duality conjectures for supersymmetric gauge theories. We perform tests of mirror symmetry of three-dimensional quiver gauge theories and of Seiberg-like dualities. Specifically, we explicitly show that the partition functions of the dual pairs, which are highly nontrivial functions of the deformations, agree. We describe extensions of these dualities which can be inferred from the form of the partition functions. We review the application of the matrix model to the study of renormalization group flow and the space of conformal field theories in three dimensions.</p> https://resolver.caltech.edu/CaltechTHESIS:05312012-204458381Symmetries in Three-Dimensional Superconformal Quantum Field Theories
https://resolver.caltech.edu/CaltechTHESIS:05112012-122450178
Year: 2012
DOI: 10.7907/61EK-5K70
<p>Many examples of gauge-gravity duality and quantum equivalences of different-looking three-dimensional Quantum Field Theories indicate the existence of continuous symmetries whose currents are not built from elementary, or perturbative, elds used to write down the Lagrangian. These symmetries are called hidden or nonperturbative.</p>
<p>We describe a method for studying continuous symmetries in a large class of three-dimensional supersymmetric gauge theories which, in particular, enables one to explore nonperturbative global symmetries and supersymmetries. As an application of the method, we prove conjectured supersymmetry enhancement in strongly coupled ABJM theory from N = 6 to N = 8 and nd additional nonperturbative evidence for its duality to the N = 8 U(N) SYM theory for the minimal value of the Chern-Simons coupling. Hidden supersymmetry is also shown to occur in N = 4 d = 3 SQCD with one fundamental and one adjoint hypermultiplets. An innite family of N = 6 d = 3 ABJ theories is proved to have hidden N = 8 superconformal symmetry and hidden parity on the quantum level. We test several conjectural dualities between ABJ theories and theories proposed by Bagger and Lambert, and Gustavsson by comparing superconformal indices of these theories. Comparison of superconformal indices is also used to test dualities between N = 2 d = 3 theories proposed by Aharony, the analysis of whose chiral rings teaches some general lessons about nonperturbative chiral operators of strongly coupled 3d supersymmetric gauge theories.</p>
<p>As another application of our method we consider examples of hidden global symmetries in a class of quiver three-dimensional N = 4 superconformal gauge theories. Finally, we point out to the relations between some basic properties of superconformal N = 6 theories
and their symmetries.</p>
<p>The results presented in this thesis were obtained in a series of papers [1, 2, 3, 4, 5].</p>https://resolver.caltech.edu/CaltechTHESIS:05112012-122450178Localization and Dualities in Three Dimensional Superconformal Field Theories
https://resolver.caltech.edu/CaltechTHESIS:05312012-151945114
Year: 2012
DOI: 10.7907/F9V6-HD05
<p>In this thesis we apply the technique of localization to three-dimensional N=2 superconformal field theories. We consider both theories which are exactly superconformal, and those which are believed to flow to nontrivial superconformal fixed points, for which we consider implicitly these fixed points. We find that in such theories, the partition function and certain supersymmetric observables, such as Wilson loops, can be computed exactly by a matrix model. This matrix model consists of an integral over g, the Lie algebra of the gauge group of the theory, of a certain product of 1-loop factors and classical contributions. One can also consider a space of supersymmetric deformations of the partition function corresponding to the set of abelian global symmetries.</p>
<p>In the second part of the thesis we apply these results to test dualities. We start with the case of ABJM theory, which is dual to M-theory on an asymptotically AdS_4xS^7 background. We extract strong coupling results in the field theory, which can be compared to semiclassical, weak coupling results in the gravity theory, and a nontrivial agreement is found. We also consider several classes of dualities between two three-dimensional field theories, namely, 3D mirror symmetry, Aharony duality, and Giveon-Kutasov duality. Here the dualities are typically between the IR limits of two Yang-Mills theories, which are strongly coupled in three dimensions since Yang-Mills theory is asymptotically free here. Thus the comparison is again very nontrivial, and relies on the exactness of the localization computation. We also compare the deformed partition functions, which tests the mapping of global symmetries of the dual theories. Finally, we discuss some recent progress in the understanding of general three-dimensional theories in the form of the F-theorem, a conjectured analogy to the a-theorem in four dimensions and c-theorem in two dimensions, which is closely related to the localization computation.</p>https://resolver.caltech.edu/CaltechTHESIS:05312012-151945114Searches for New Symmetries in pp Collisions with the Razor Kinematic Variables at √s = 7 TeV
https://resolver.caltech.edu/CaltechTHESIS:05072013-174540453
Year: 2013
DOI: 10.7907/B0MD-F026
<p>The construction and LHC phenomenology of the razor variables M<sub>R</sub>, an event-by-event indicator of the heavy particle mass scale, and R, a dimensionless variable related to the transverse momentum imbalance of events and missing transverse energy, are presented. The variables are used in the analysis of the first proton-proton collisions dataset at CMS (35 pb<sup>-1</sup>) in a search for superpartners of the quarks and gluons, targeting indirect hints of dark matter candidates in the context of supersymmetric theoretical frameworks. The analysis produced the highest sensitivity results for SUSY to date and extended the LHC reach far beyond the previous Tevatron results. A generalized inclusive search is subsequently presented for new heavy particle pairs produced in √s = 7 TeV proton-proton collisions at the LHC using 4.7±0.1 fb<sup>-1</sup> of integrated luminosity from the second LHC run of 2011. The selected events are analyzed in the 2D razor-space of M<sub>R</sub> and R and the analysis is performed in 12 tiers of all-hadronic, single and double leptons final states in the presence and absence of b-quarks, probing the third generation sector using the event heavy-flavor content. The search is sensitive to generic supersymmetry models with minimal assumptions about the superpartner decay chains. No excess is observed in the number or shape of event yields relative to Standard Model predictions. Exclusion limits are derived in the CMSSM framework with gluino masses up to 800 GeV and squark masses up to 1.35 TeV excluded at 95% confidence level, depending on the model parameters. The results are also interpreted for a collection of simplified models, in which gluinos are excluded with masses as large as 1.1 TeV, for small neutralino masses, and the first-two generation squarks, stops and sbottoms are excluded for masses up to about 800, 425 and 400 GeV, respectively. </p>
<p>With the discovery of a new boson by the CMS and ATLAS experiments in the γ-γ and 4 lepton final states, the identity of the putative Higgs candidate must be established through the measurements of its properties. The spin and quantum numbers are of particular importance, and we describe a method for measuring the J<sup>PC</sup> of this particle using the observed signal events in the H to ZZ<sup>*</sup> to 4 lepton channel developed before the discovery. Adaptations of the razor kinematic variables are introduced for the H to WW<sup>*</sup> to 2 lepton/2 neutrino channel, improving the resonance mass resolution and increasing the discovery significance. The prospects for incorporating this channel in an examination of the new boson J<sup>PC</sup> is discussed, with indications that this it could provide complementary information to the H to ZZ<sup>*</sup> to 4 lepton final state, particularly for measuring CP-violation in these decays.</p>https://resolver.caltech.edu/CaltechTHESIS:05072013-174540453Branes and Supersymmetric Quantum Field Theories
https://resolver.caltech.edu/CaltechTHESIS:01242014-104001899
Year: 2014
DOI: 10.7907/Y1VH-E821
<p>Since the discovery of D-branes as non-perturbative, dynamic objects in string theory, various configurations of branes in type IIA/B string theory and M-theory have been considered to study their low-energy dynamics described by supersymmetric quantum field theories.</p>
<p>One example of such a construction is based on the description of Seiberg-Witten curves of four-dimensional N = 2 supersymmetric gauge theories as branes in type IIA string theory and M-theory. This enables us to study the gauge theories in strongly-coupled regimes. Spectral networks are another tool for utilizing branes to study non-perturbative regimes of two- and four-dimensional supersymmetric theories. Using spectral networks of a Seiberg-Witten theory we can find its BPS spectrum, which is protected from quantum corrections by supersymmetry, and also the BPS spectrum of a related two-dimensional N = (2,2) theory whose (twisted) superpotential is determined by the Seiberg-Witten curve. When we don’t know the perturbative description of such a theory, its spectrum obtained via spectral networks is a useful piece of information. In this thesis we illustrate these ideas with examples of the use of Seiberg-Witten curves and spectral networks to understand various two- and four-dimensional supersymmetric theories.</p>
<p>First, we examine how the geometry of a Seiberg-Witten curve serves as a useful tool for identifying various limits of the parameters of the Seiberg-Witten theory, including Argyres-Seiberg duality and Argyres-Douglas fixed points. Next, we consider the low-energy limit of a two-dimensional N = (2, 2) supersymmetric theory from an M-theory brane configuration whose (twisted) superpotential is determined by the geometry of the branes. We show that, when the two-dimensional theory flows to its infra-red fixed point, particular cases realize Kazama-Suzuki coset models. We also study the BPS spectrum of an Argyres-Douglas type superconformal field theory on the Coulomb branch by using its spectral networks. We provide strong evidence of the equivalence of superconformal field theories from different string-theoretic constructions by comparing their BPS spectra.</p>https://resolver.caltech.edu/CaltechTHESIS:01242014-104001899Three-Dimensional Superconformal Field Theory, Chern-Simons Theorv, and Their Correspondence
https://resolver.caltech.edu/CaltechTHESIS:06062014-152022421
Year: 2014
DOI: 10.7907/7CA7-9C79
In this thesis, we discuss 3d-3d correspondence between Chern-Simons theory and three-dimensional N = 2 superconformal field theory. In the 3d-3d correspondence proposed by Dimofte-Gaiotto-Gukov information of abelian flat connection in Chern-Simons theory was not captured. However, considering M-theory configuration giving the 3d-3d correspondence and also other several developments, the abelian flat connection should be taken into account in 3d-3d correspondence. With help of the homological knot invariants, we construct 3d N = 2 theories on knot complement in 3-sphere for several simple knots. Previous theories obtained by Dimofte-Gaiotto-Gukov can be obtained by Higgsing of the full theories. We also discuss the importance of all flat connections in the 3d-3d correspondence by considering boundary conditions in 3d N = 2 theories and 3-manifold.https://resolver.caltech.edu/CaltechTHESIS:06062014-152022421Search for Higgs Boson Production Beyond the Standard Model Using the Razor Kinematic Variables in pp Collisions at √s=8 TeV and Optimization of Higgs Boson Identification Using a Quantum Annealer
https://resolver.caltech.edu/CaltechTHESIS:05052015-155442785
Year: 2015
DOI: 10.7907/Z9XK8CHR
<p>In the first part of this thesis we search for beyond the Standard Model physics through the search for anomalous production of the Higgs boson using the razor kinematic variables. We search for anomalous Higgs boson production using proton-proton collisions at center of mass energy √s=8 TeV collected by the Compact Muon Solenoid experiment at the Large Hadron Collider corresponding to an integrated luminosity of 19.8 fb<sup>-1</sup>.</p>
<p>In the second part we present a novel method for using a quantum annealer to train a classifier to recognize events containing a Higgs boson decaying to two photons. We train that classifier using simulated proton-proton collisions at √s=8 TeV producing either a Standard Model Higgs boson decaying to two photons or a non-resonant Standard Model process that produces a two photon final state.</p>
<p>The production mechanisms of the Higgs boson are precisely predicted by the Standard Model based on its association with the mechanism of electroweak symmetry breaking. We measure the yield of Higgs bosons decaying to two photons in kinematic regions predicted to have very little contribution from a Standard Model Higgs boson and search for an excess of events, which would be evidence of either non-standard production or non-standard properties of the Higgs boson. We divide the events into disjoint categories based on kinematic properties and the presence of additional b-quarks produced in the collisions. In each of these disjoint categories, we use the razor kinematic variables to characterize events with topological configurations incompatible with typical configurations found from standard model production of the Higgs boson.</p>
<p>We observe an excess of events with di-photon invariant mass compatible with the Higgs boson mass and localized in a small region of the razor plane. We observe 5 events with a predicted background of 0.54 ± 0.28, which observation has a p-value of 10<sup>-3</sup> and a local significance of 3.35σ. This background prediction comes from 0.48 predicted non-resonant background events and 0.07 predicted SM higgs boson events. We proceed to investigate the properties of this excess, finding that it provides a very compelling peak in the di-photon invariant mass distribution and is physically separated in the razor plane from predicted background. Using another method of measuring the background and significance of the excess, we find a 2.5σ deviation from the Standard Model hypothesis over a broader range of the razor plane.</p>
<p>In the second part of the thesis we transform the problem of training a classifier to distinguish events with a Higgs boson decaying to two photons from events with other sources of photon pairs into the Hamiltonian of a spin system, the ground state of which is the best classifier. We then use a quantum annealer to find the ground state of this Hamiltonian and train the classifier. We find that we are able to do this successfully in less than 400 annealing runs for a problem of median difficulty at the largest problem size considered. The networks trained in this manner exhibit good classification performance, competitive with the more complicated machine learning techniques, and are highly resistant to overtraining. We also find that the nature of the training gives access to additional solutions that can be used to improve the classification performance by up to 1.2% in some regions.</p>https://resolver.caltech.edu/CaltechTHESIS:05052015-1554427853d-3d Correspondence for Seifert Manifolds
https://resolver.caltech.edu/CaltechTHESIS:05282016-191214961
Year: 2016
DOI: 10.7907/Z9X34VF9
<p>In this dissertation, we investigate the 3d-3d correspondence for Seifert manifolds. This correspondence, originating from string theory and M-theory, relates the dynamics of three-dimensional quantum field theories with the geometry of three-manifolds.</p>
<p>We first start in Chapter II with the simplest cases and demonstrate the extremely rich interplay between geometry and physics even when the manifold is just a direct product. In this particular case, by examining the problem from various vantage points, we generalize the celebrated relations between 1) the Verlinde algebra, 2) quantum cohomology of the Grassmannian, 3) quantization of Chern-Simons theory and 4) the index theory of the moduli space of flat connections to a completely new set of relations between 1) the "equivariant Verlinde algebra" for a complex group, 2) the equivariant quantum K-theory of the vortex moduli space, 3) quantization of complex Chern-Simons theory and 4) the equivariant index theory of the moduli space of Higgs bundles.</p>
<p>In Chapter III we move one step up in complexity by looking at the next simplest three-manifolds---lens spaces. We test the 3d-3d correspondence for theories that are labeled by lens spaces, reaching a full agreement between the index of the 3d N=2 "lens space theory" and the partition function of complex Chern-Simons theory on the lens space.</p>
<p>The two different types of manifolds studied in the previous two chapters also have interesting interactions. We show in Chapter IV the equivalence between two seemingly distinct 2d TQFTs: one comes from the "Coulomb branch index" of the class S theory on a lens space, the other is the "equivariant Verlinde formula". We check this relation explicitly for SU(2) and demonstrate that the SU(N) equivariant Verlinde algebra can be derived using field theory via (generalized) Argyres-Seiberg dualities.</p>
<p>In the last chapter, we directly jump to the most general situation, giving a proposal for the 3d-3d correspondence for an arbitrary Seifert manifold. We remark on the huge class of novel dualities relating different descriptions of the "Seifert theory" associated with the same Seifert manifold and suggest ways that our proposal could be tested.</p>https://resolver.caltech.edu/CaltechTHESIS:05282016-191214961Boundary Relative Entropy as Quasilocal Energy: Positive Energy Theorems and Tomography
https://resolver.caltech.edu/CaltechTHESIS:06072016-152814803
Year: 2016
DOI: 10.7907/Z9ZW1HW3
We argue that for a spherical region R on the boundary, relative entropy between the vacuum and an arbitrary holographic excited state can be computed in the bulk as a quasilocal energy associated to the volume between R and the minimal surface B̃ ending on the boundary ∂R. Since relative entropy is monotonic and positive in any well-defined quantum theory, the associated quasilocal energy must also be positive and monotonic. This gives rise to an infinite number of constraints on the gravitational bulk, which must be satisfied in any theory of quantum gravity with a well-defined UV completion. For small regions $R$, these constraints translate into integrated positivity conditions of the bulk stress-energy tensor. When the bulk is Einstein gravity coupled to scalar fields, the boundary relative entropy can be related to an integral of the bulk action on the minimal surface B̃. Near the boundary, this expression can be inverted via the inverse Radon transform, to obtain the bulk stress energy tensor at a point in terms of the boundary relative entropy.https://resolver.caltech.edu/CaltechTHESIS:06072016-152814803Naturalness Confronts Nature: Searches for Supersymmetry with the CMS Detector in pp Collisions at √s = 8 and 13 TeV
https://resolver.caltech.edu/CaltechTHESIS:08232016-112522351
Year: 2017
DOI: 10.7907/Z9GX48JV
In this thesis, we present two inclusive searches for supersymmetric particles at 8 and 13 TeV using the razor variables and guided by the principle of naturalness. We build a framework to explore the natural supersymmetry parameter space of gluino and top squark masses and branching ratios, which is a unique attempt to cover this parameter space in a more complete way than ever before using LHC data. With this approach, the production of top squarks and gluinos are excluded below 700 GeV and 1.6 TeV, respectively, independent of the branching ratios, constituting one of the tightest constraints on natural supersymmetry from the LHC. Motivated by the need to mitigate the effects of multiple interactions per bunch crossing (pileup), an essential feature of present and future hadron colliders, in this thesis we also study the precision timing capabilities of a LYSO-based sampling calorimeter, and achieve a time resolution of 30 ps in electron test beam measurements. The achieved resolution corresponds to the precision needed to significantly reduce the inclusion of pileup particles in the reconstruction of the event of interest. This study is foundational in building an R and D program on precision timing for the high-luminosity LHC and other future hadron colliders. We also propose alternative simplified models to study Higgs-plus-jets events at the LHC, and reinterpret an excess observed at 8 TeV in the context of these models. Finally, we discuss a search for narrow resonances in the dijet mass spectrum at 13 TeV using the data-scouting technique at CMS, which records a smaller event format to increase the maximum recordable rate. For the benchmark models with a vector or axial-vector mediator that couples to quarks and dark matter particles, the dijet search excludes mediator masses from 0.5 TeV up to 2.7 TeV largely independent of the dark matter particle mass, which constitutes a larger exclusion than traditional mono-X searches at the LHC. In the plane of the dark matter-nucleon interaction cross section versus dark matter mass, the dijet search is also more sensitive than direct detection experiments for spin-dependent cross sections.https://resolver.caltech.edu/CaltechTHESIS:08232016-112522351Searches for New Physics at the Compact Muon Solenoid Experiment and Precision Timing Calorimetry
https://resolver.caltech.edu/CaltechTHESIS:05192017-195511866
Year: 2017
DOI: 10.7907/Z9MK69Z6
<p>In this thesis, we present several searches for beyond the standard model physics in proton-proton collisions recorded by the Compact Muon Solenoid Experiment at center-of-mass energy of 8 and 13\TeV. We search for particle dark matter in events with two or more jets and missing transverse momentum at $\sqrt{s} = 8$ TeV, in this search we use the razor variables to discriminate signal from background events and thus improve the overall sensitivity of the analysis. We observe agreement between the observation and the background estimation. The interpretation of the results is carried out in the context of an effective field theory that couples the standard model quarks to the dark matter candidate. A search for anomalous production of Higgs bosons using 15.3 $\mathrm{fb}^{-1}$ of proton-proton collisions at $\sqrt{s} = 13$ TeV is also presented; this search selects events with a Higgs boson in association with jets, where the Higgs candidate decays into two photons. We also employ the razor variables ($\mathrm{M_{R}}, \mathrm{R}^{2}$) to discriminate signal from background. We observe an excess of events in one of the search bins with relatively high values of $\mathrm{M_{R}}$ and $\mathrm{R}^{2}$. The interpretation of this analysis is pair production of bottom squarks in the context of supersymmetry, this model is also presented in one of the appendices of this thesis. In the other appendix of this thesis, we present a search for new phenomena in high-mass diphoton events using 12.9 $\mathrm{fb}^{-1}$ of proton-proton collisions at $\sqrt{s} = 13$ TeV. This search observed a significant excess (3.4 standard deviations, local) with 2015 data at a diphoton invariant mass of 750 GeV, equivalent to $\approx$ 20\% of the current dataset. By repeating the search with the larger dataset collected in 2016, we found that the aforementioned excess has been greatly disfavored. Additionally, in order to confirm the robustness and correctness of the data analysis techniques used in this search, we have carried out a second -- completely independent -- analysis, which confirms the absence of an excess at a diphoton invariant mass of 750 GeV.</p>
<p>We also present detector research and developments studies of electromagnetic calorimeters equipped with precision timing capabilities. We present several calorimeter prototypes that were tested at the Fermilab Test Beam Facility. These prototypes include LYSO-based calorimeters, tungsten-LYSO "shashlik" sampling calorimeters, micro-channel-plate sampling calorimeters, and silicon-based sampling calorimeters. The results of these studies indicate that time resolutions of the order of $\sim$ 30 ps are readily available when measuring electromagnetic showers. A discussion about the applications of precision timing in high energy physics experiments is also presented, with a particular interest in pileup rejection in the context of the high-luminosity upgrade of the Large Hadron Collider foreseen to start in 2025.</p>https://resolver.caltech.edu/CaltechTHESIS:05192017-195511866Knots, Trees, and Fields: Common Ground Between Physics and Mathematics
https://resolver.caltech.edu/CaltechTHESIS:07282016-144651775
Year: 2017
DOI: 10.7907/Z9VX0DHZ
<p>One main theme of this thesis is a connection between mathematical physics (in particular, the three-dimensional topological quantum field theory known as Chern-Simons theory) and three-dimensional topology. This connection arises because the partition function of Chern-Simons theory provides an invariant of three-manifolds, and the Wilson-loop observables in the theory define invariants of knots. In the first chapter, we review this connection, as well as more recent work that studies the classical limit of quantum Chern-Simons theory, leading to relations to another knot invariant known as the <math>A</math>-polynomial. (Roughly speaking, this invariant can be thought of as the moduli space of flat <math>SL(2,<bt>C</bt>)</math> connections on the knot complement.) In fact, the connection can be deepened: through an embedding into string theory, categorifications of polynomial knot invariants can be understood as spaces of BPS states.</p>
<p>We go on to study these homological knot invariants, and interpret spectral sequences that relate them to one another in terms of perturbations of supersymmetric theories. Our point is more general than the application to knots; in general, when one perturbs any modulus of a supersymmetric theory and breaks a symmetry, one should expect a spectral sequence to relate the BPS states of the unperturbed and perturbed theories. We consider several diverse instances of this general lesson. In another chapter, we consider connections between supersymmetric quantum mechanics and the de Rham version of homotopy theory developed by Sullivan; this leads to a new interpretation of Sullivan's minimal models, and of Massey products as vacuum states which are entangled between different degrees of freedom in these models.</p>
<p>We then turn to consider a discrete model of holography: a Gaussian lattice model defined on an infinite tree of uniform valence. Despite being discrete, the matching of bulk isometries and boundary conformal symmetries takes place as usual; the relevant group is <math>PGL(2,<bt>Q</bt><sub>p</sub>)</math>, and all of the formulas developed for holography in the context of scalar fields on fixed backgrounds have natural analogues in this setting. The key observation underlying this generalization is that the geometry underlying AdS<sub>3</sub>/CFT<sub>2</sub> can be understood algebraically, and the base field can therefore be changed while maintaining much of the structure. Finally, we give some analysis of <math>A</math>-polynomials under change of base (to finite fields), bringing things full circle.</p>https://resolver.caltech.edu/CaltechTHESIS:07282016-144651775A Symphony of Supersymmetry and Geometry: Invariants, Dualities and Chiral Rings
https://resolver.caltech.edu/CaltechTHESIS:05032018-153255038
Year: 2018
DOI: 10.7907/K2K2-9790
<p>The present dissertation discusses aspects of supersymmetric quantum field theory, whose main themes are two-folded. First, we explore connections between superconformal theories in various dimensions and geometric invariants. Such correspondence arises from compactification of string theory or M-theory, which encodes geometric quantities into physical observables. Second, we study in detail the chiral rings and their quantum corrections in certain supersymmetric gauge theory. The goal is to shed some light on the hitherto mysterious electric-magnetic dualities.</p>
<p>We first consider M5 brane on the product manifold <i>L</i>(<i>k</i>, 1) × <i>M</i><sub>3</sub>, where <i>M</i><sub>3</sub> = <i>L</i>(<i>p</i>, 1). Compactification on <i>L</i>(<i>p</i>, 1) gives rise to three dimensional theory <i>T</i>[<i>L</i>(<i>p</i>, 1)] whose partition function, according to 3d-3d correspondence, is equivalent to Chern-Simons invariants with complex gauge group on <i>L</i>(<i>p</i>, 1). We test the statement in Chapter 2 by taking <i>k</i> = 0 and calculating the supersymmetric index. We find a full agreement between two seemingly distinct quantities. In particular, when <i>p</i> = 1, we see the familiar <i>S</i><sup>3</sup> partition function of Chern-Simons theory arises from the index of a free theory.</p>
<p>We then move on in Chapter 3 to consider <i>M</i><sub>3</sub> = <i>S</i><sup>1</sup> × Σ, and twisted compactification on general Riemann surface Σ with tame punctures. The twisted partition function of lens space theory <i>T</i>[<i>L</i>(<i>k</i>, 1)] on <i>S</i><sup>1</sup> × Σ computes the graded dimension of the Hilbert space after geometrically quantizing Hitchin moduli space <i>M</i><sub>H</sub>, dubbed as "tame Hitchin characters" or "equivariant Verlinde formula". We show that this quantity can be computed from the "Coulomb branch index" of the class <i>S</i> theory <i>T</i>[Σ] on <i>L</i>(<i>k</i>, 1) × <i>S</i><sup>1</sup>. The gauge groups on two sides of the equivalence are naturally <i>G</i> and the Langlands dual group <sup><i>L</i></sup><i>G</i>. We check explicitly the relation for <i>G</i> = <i>SU</i>(2) or <i>SO</i>(3). We also consider more general case where <i>G</i> is <i>SU</i>(<i>N</i>) or <i>PSU</i>(<i>N</i>) and show that the <i>SU</i>(<i>N</i>) equivariant Verlinde formula can be derived using field theory via (generalized) Argyres-Seiberg duality.</p>
<p>As a further application, in Chapter 4 we use Coulomb branch indices of Argyres-Douglas theories on <i>S</i><sup>1</sup> × <i>L</i>(<i>k</i>, 1) to quantize moduli spaces <i>M</i><sub>H</sub> of wild/irregular Hitchin systems. We obtain the "wild Hitchin characters", and observe that the characters can always be written as a sum over fixed points in <i>M</i><sub>H</sub> under the <i>U</i>(1) Hitchin action, and a limit of them can be identified with matrix elements of the vii modular transform <i>ST<sup>k</sup>S</i> in certain vertex operator algebras. The appearance of vertex operator algebras, which was known previously to be associated with Schur operators but not Coulomb branch operators, is somewhat surprising.</p>
<p>The BPS spectrum of superconformal theories probe the geometry of Hitchin moduli space. Conversely, physical data of superconformal theories can be read off from Hitchin moduli space as well. We study this dictionary in Chapter 5 for general Argyres-Douglas theories and obtain a refined classification. We also discuss the S-duality of these theories, and find that the weakly coupled descriptions are given by the degeneration limit of auxiliary Riemann sphere with marked points.</p>
<p>Finally, in Chapter 6, we analyze classical and quantum chiral ring relations of four dimensional <i>N</i> = 1 adjoint SQCD with superpotential turned on for the adjoint field. In particular, for the mass deformed theory we obtain the complete on-shell vacuum expectation value for various gauge invariant chiral operators and find non trivial gaugino condensations. We argue that the solution of the chiral ring is in one-to-one correspondence with supersymmetric vacua, provided that an additional Konishi anomaly equation is included.</p>https://resolver.caltech.edu/CaltechTHESIS:05032018-153255038Supersymmetric Scattering Amplitudes and Algebraic Aspects of Holography from the Projective Line
https://resolver.caltech.edu/CaltechTHESIS:06102019-125514401
Year: 2019
DOI: 10.7907/HFPD-JX10
<p>In this thesis, we consider two topics in string theory and quantum field theory which are related by the common appearance of one-dimensional projective geometry. In the first half of the thesis, we study six-dimensional (6D) supersymmetric quantum field theories and supergravity at the leading (tree) approximation and compute the complete S-matrix for these theories as world-sheet integrals over the punctured Riemann sphere. This exploits the analytic structure of tree amplitudes which are rational and holomorphic in the kinematics and naturally related to the geometry of points on the complex projective line. The 6D n-particle S-matrix makes many symmetries and hidden properties manifest and generalizes the well-studied formulas for four-dimensional amplitudes in the form of twistor string theory and the rational curves formalism. While the systems we study are all field theories, they are in essence low-energy effective field theory limits of string theory and M-theory backgrounds. This includes theories such as those with 6D (2,0) supersymmetry which contain U(1) self-dual tensor fields which are difficult to treat from a Lagrangian point of view. Our formulas circumvent this difficulty and allow a generalization and unification of a large class of 6D scattering amplitudes which permit a sensible classical limit, including the abelian world-volume of the M-theory Five-brane. Dimensional reduction to four dimensions is also possible, leading to new formulas for 4D physics from 6D. </p>
<p>In the second half of the thesis, we discuss the projective algebraic and geometric structure of the AdS<sub>3</sub>/CFT<sub>2</sub> correspondence. In the usual statement of this correspondence, two-dimensional conformal field theory (CFT) on the Riemann sphere or a higher-genus surface is holographically dual to features of topological gravity in three dimensions with negative curvature. Since every compact Riemann surface is a projective algebraic curve, many constructions of interest in physics (which a priori depend on the analytic structure of the spacetime) can be formulated in purely algebraic language. We generalize the AdS (anti-de Sitter space)/CFT correspondence according to this principle using projective geometry over the p-adic numbers, Q<sub>p</sub>. The result is a formulation of holography in which the bulk geometry is discrete---the Bruhat--Tits tree for PGL(2,Q<sub>p</sub>)---but the group of bulk isometries nonetheless agrees with that of boundary conformal transformations and is not broken by discretization. Parallel to the usual holographic correspondence, semi-classical dynamics of fields in the bulk compute the correlation functions of local operators on the boundary. Beyond correlators on the p-adic line, we propose a tensor network model in which the patterns of entanglement on the boundary are computed by discrete geometries in the bulk. We suggest that this forms the natural geometric setting for tensor networks that have been proposed as models of bulk reconstruction via quantum error correcting codes. The model is built from tensors based on projective geometry over finite fields, F<sub>p</sub>, and correctly computes the Ryu-Takayanagi formula, holographic entanglement and black hole entropy, and multiple interval entanglement inequalities.</p>
<p>In Chapter 2, we present tree-level n-particle on-shell scattering amplitudes of various brane theories with 16 conserved supercharges which are generalizations of Dirac--Born--Infeld theory. These include the world-volume theory of a probe D3-brane or D5-brane in 10D Minkowski spacetime as well as a probe M5-brane in 11D Minkowski spacetime, which describes self interactions of an abelian tensor supermultiplet with 6D (2,0) supersymmetry. We propose twistor-string-like formulas for tree-level scattering amplitudes of all multiplicities for each of these theories, and the amplitudes are written as integrals over the moduli space of certain rational maps localized on the (n-3)! solutions of the scattering equations. The R symmetry of the D3-brane theory is shown to be SU(4) x U(1), and the U(1) factor implies that its amplitudes are helicity conserving. Each of 6D theories (D5-brane and M5-brane) reduces to the D3-brane theory by dimensional reduction. As special cases of the general M5-brane amplitudes, we present compact formulas for examples involving only the self-dual B field with n=4,6,8.</p>
<p>In Chapter 3, we extend this formalism to n-particle tree-level scattering amplitudes of six-dimensional N=(1,1) super Yang--Mills (SYM) and N=(2,2) supergravity (SUGRA). The SYM theory arises on the world volume of coincident D5-branes, and the supergravity is the result of toroidal compactification of string theory. These theories have non-abelian interactions which allow for both even and odd-point amplitudes, unlike the branes of Chapter 2. Due to the properties of spinor-helicity variables in six dimensions, the even-n and odd-n formulas are quite different and have to be treated separately. We first propose a manifestly supersymmetric expression for the even-n amplitudes of N=(1,1) SYM theory and perform various consistency checks. By considering soft-gluon limits of the even-n amplitudes, we deduce the form of the rational maps and the integrand for n odd. The odd-n formulas obtained in this way have a new redundancy that is intertwined with the usual SL(2,C) invariance on the Riemann sphere. We also propose an alternative form of the formulas, analogous to the Witten--RSV (Roiban, Spradlin, and Volovich) formulation, and explore its relationship with the symplectic (or Lagrangian) Grassmannian. Since the amplitudes are formulated in a way that manifests double-copy properties, formulas for the six-dimensional N=(2,2) SUGRA amplitudes follow. These six-dimensional results allow us to deduce new formulas for five-dimensional SYM and SUGRA amplitudes, as well as massive amplitudes of four-dimensional N=4 SYM on the Coulomb branch.</p>
<p>In Chapter 4, we consider half-maximal supergravity and present a twistor-like formula for the complete tree-level S matrix of chiral 6D (2,0) supergravity coupled to 21 abelian tensor multiplets. This is the low-energy effective theory that corresponds to Type IIB superstring theory compactified on a K3 surface. As in previous chapters, the formula is expressed as an integral over the moduli space of certain rational maps of the punctured Riemann sphere; the new ingredient is an integrand which successfully incorporates both gravitons and multiple flavors of tensors. By studying soft limits of the formula, we are able to explore the local moduli space of this theory, SO(5,21)/(SO(5) x SO(21)). Finally, by dimensional reduction, we also obtain a new formula for the tree-level S-matrix of 4D N=4 Einstein--Maxwell theory.</p>
<p>In Chapter 5, we introduce p-adic AdS/CFT and discuss several physical and mathematical features of the holographic correspondence between conformal field theories on P<sup>1</sup>(Q<sub>p</sub>) and lattice models on the Bruhat--Tits tree of PGL(2,Q<sub>p</sub>), an infinite tree of p+1 valence which has the p-adic projective line as its boundary. We review the p-adic numbers, the Bruhat--Tits tree, and some of their applications to physics including p-adic CFT. A key feature of these constructions is the discrete and hierarchical nature of the tree and the corresponding field theories, which serve as a toy model of holography in which there are no gravitons and no conformal descendants. Standard holographic results for massive free scalar fields in a fixed background carry over to the tree; semi-classical dynamics in the bulk compute correlation functions in the dual field theory and we obtain a precise relationship between the bulk mass and the scaling dimensions of local operators. It is also possible to interpret the vertical direction in the tree a renormalization-group scale for modes in the boundary CFT. Higher-genus bulk geometries (the BTZ black hole and its generalizations) can be understood straightforwardly in our setting and their construction parallels the story in AdS_3 topological gravity.</p>
<p>In Chapter 6, we consider a class of holographic quantum error-correcting codes, built from perfect tensors in network configurations dual to Bruhat--Tits trees and their quotients by Schottky groups corresponding to BTZ black holes. The resulting holographic states can be constructed in the limit of infinite network size. We obtain a p-adic version of entropy which obeys a Ryu--Takayanagi like formula for bipartite entanglement of connected or disconnected regions, in both genus-zero and genus-one p-adic backgrounds, along with a Bekenstein--Hawking-type formula for black hole entropy. We prove entropy inequalities obeyed by such tensor networks, such as subadditivity, strong subadditivity, and monogamy of mutual information (which is always saturated). In addition, we construct infinite classes of perfect tensors directly from semi-classical states in phase spaces over finite fields, generalizing the CRSS algorithm. These codes and the resulting networks provide a natural bulk geometric interpretation of non-Archimedean notions of entanglement in holographic boundary states.</p>https://resolver.caltech.edu/CaltechTHESIS:06102019-125514401Effective Field Theory Topics in the Modern S-Matrix Program
https://resolver.caltech.edu/CaltechTHESIS:05262021-204932248
Year: 2021
DOI: 10.7907/qg7a-7n08
<p>Quantum field theory is the most predictive theory of nature ever tested, yet the scattering amplitudes produced from the standard application of Lagrangians and Feynman rules belie the simplicity of the underlying physics, obscuring the physical answers behind off-shell actions and gauge redundant descriptions. The aim of the modern S-matrix program (or the "amplitudes" subfield) is to reformulate specific field theories and manifest underlying structures in order to make high multiplicity and/or high loop scattering calculations tractable.</p>
<p>Many of the systems amenable to amplitudes techniques are actually intimately related to each other through the double-copy relations. We argue that conformal invariance is common thread linking several of the scalar effective field theories appearing in the double copy. For a derivatively coupled scalar with a quartic <i>O</i>(<i>p</i>⁴) vertex, classical conformal invariance dictates an infinite tower of additional interactions that coincide exactly with Dirac-Born-Infeld theory analytically continued to spacetime dimension <i>D</i> = 0. For the case of a quartic <i>O</i>(<i>p</i>⁶) vertex, classical conformal invariance constrains the theory to be the special Galileon in <i>D</i> = -2 dimensions. We also verify the conformal invariance of these theories by showing that their amplitudes are uniquely fixed by the conformal Ward identities. In these theories, conformal invariance is a much more stringent constraint than scale invariance.</p>
<p>Although many of the theories in the double-copy admit a high degree of space-time symmetry, amplitudes tools can be applied to non-relativistic theories as well. We explore the scattering amplitudes of fluid quanta described by the Navier-Stokes equation and its non-Abelian generalization. These amplitudes exhibit universal infrared structures analogous to the Weinberg soft theorem and the Adler zero. Furthermore, they satisfy on-shell recursion relations which together with the three-point scattering amplitude furnish a pure S-matrix formulation of incompressible fluid mechanics. Remarkably, the amplitudes of the non-Abelian Navier-Stokes equation also exhibit color-kinematics duality as an off-shell symmetry, for which the associated kinematic algebra is literally the algebra of spatial diffeomorphisms. Applying the double copy prescription, we then arrive at a new theory of a tensor bi-fluid. Finally, we present monopole solutions of the non-Abelian and tensor Navier-Stokes equations and observe a classical double copy structure.</p>https://resolver.caltech.edu/CaltechTHESIS:05262021-204932248