Advisor Feed
https://feeds.library.caltech.edu/people/Ooguri-H/advisor.rss
A Caltech Library Repository Feedhttp://www.rssboard.org/rss-specificationpython-feedgenenThu, 30 Nov 2023 19:49:46 +0000D-Branes in Anti-de-Sitter Space
https://resolver.caltech.edu/CaltechETD:etd-06022003-200011
Authors: Lee, Peter Byungho
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://thesis.library.caltech.edu/id/eprint/2380String/Gauge Duality and Penrose Limit
https://resolver.caltech.edu/CaltechETD:etd-05152003-134850
Authors: Park, Jongwon
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://thesis.library.caltech.edu/id/eprint/1812Large N Dualities in Topological String Theory
https://resolver.caltech.edu/CaltechETD:etd-05232005-184326
Authors: Okuda, Takuya
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://thesis.library.caltech.edu/id/eprint/1977Aspects of Topological String Theory
https://resolver.caltech.edu/CaltechETD:etd-05272008-225257
Authors: Cook, Paul Langabi Hogan
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://thesis.library.caltech.edu/id/eprint/2174Holomorphic Anomaly Equations in Topological String Theory
https://resolver.caltech.edu/CaltechETD:etd-05302008-111309
Authors: Yang, Jie
Year: 2008
DOI: 10.7907/A7K8-8W74
<p>In this thesis we discuss various aspects of topological string theories. In particular we provide a derivation of the holomorphic anomaly equation for open strings and study aspects of the Ooguri, Strominger, and Vafa conjecture.</p>
<p>Topological string theory is a computable theory. The amplitudes of the closed topological string satisfy a holomorphic anomaly equation, which is a recursive differential equation. Recently this equation has been extended to the open topological string. We discuss the derivation of this open holomorphic anomaly equation. We find that open topological string amplitudes have new anomalies that spoil the recursive structure of the equation and introduce dependence on wrong moduli (such as complex structure moduli in the A-model), unless the disk one-point functions vanish. We also show that a general solution to the extended holomorphic anomaly equation for the open topological string on D-branes in a Calabi-Yau manifold, is obtained from the general solution to the holomorphic anomaly equations for the closed topological string on the same manifold, by shifting the closed string moduli by amounts proportional to the 't Hooft coupling.</p>
<p>An important application of closed topological string theory is the Ooguri, Strominger, and Vafa conjecture, which states that a certain black hole partition function is a product of topological and anti-topological string partition functions. However when the black hole has finite size, the relation becomes complicated. In a specific example, we find a new factorization rule in terms of a pair of functions which we interpret as the "non-perturbative' completion of the topological string partition functions.</p>https://thesis.library.caltech.edu/id/eprint/2315Topics in Supersymmetry Breaking and Gauge/Gravity Dualities
https://resolver.caltech.edu/CaltechTHESIS:05042010-150716614
Authors: Park, Chang-Soon
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://thesis.library.caltech.edu/id/eprint/5771Refined BPS Invariants, Chern-Simons Theory, and the Quantum Dilogarithm
https://resolver.caltech.edu/CaltechTHESIS:05142010-131147918
Authors: Dimofte, Tudor Dan
Year: 2010
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://thesis.library.caltech.edu/id/eprint/58084d/2d Correspondence: Instantons and W-Algebras
https://resolver.caltech.edu/CaltechTHESIS:05302012-170816705
Authors: Song, Jaewon
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://thesis.library.caltech.edu/id/eprint/7103Boundary Relative Entropy as Quasilocal Energy: Positive Energy Theorems and Tomography
https://resolver.caltech.edu/CaltechTHESIS:06072016-152814803
Authors: Stoica, Bogdan
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://thesis.library.caltech.edu/id/eprint/9852Spin in Conformal Field Theory
https://resolver.caltech.edu/CaltechTHESIS:06012018-180443792
Authors: Kravchuk, Petr
Year: 2018
DOI: 10.7907/54MW-WY30
<p>We study various questions related to operators with spin in quantum conformal field theory in dimensions higher than two. In particular, we classify conformally-invariant tensor structures which appear in correlation functions of local operators and develop tools for computation of conformal blocks which contribute to these functions. We study the crossing equations for four-point functions using numerical and analytical techniques. Finally, we explore the question of analytic continuation of local operators in spin, which leads us to a simple proof of a generalized Lorentzian inversion formula.</p>https://thesis.library.caltech.edu/id/eprint/11008Topological Invariants of Interacting Gapped Quantum Materials and Transport Phenomena
https://resolver.caltech.edu/CaltechTHESIS:06012021-025758430
Authors: Spodyneiko, Lev
Year: 2021
DOI: 10.7907/fmt8-qb23
<p>In this thesis we study transport properties of interacting lattice system focusing, on those which become topologically protected at low temperatures for gapped Hamiltonians.
We prove the vanishing of the net energy currents in
equilibrium states of lattice systems as well as systems of nonrelativistic particles with finite-range potential interactions. We derive Kubo-like formulas for the thermal and thermoelectic Hall conductances of arbitrary 2d lattice systems which are free from
ambiguities associated with the definition of magnetizations. We use these formulas to define a relative topological invariant of gapped 2d lattice systems at zero temperature.</p>
<p>We define and study analogs of the Thouless charge pump and Berry Curvature for many-body gapped systems in spatial dimension D. We show how to attach a topological invariant to a D-dimensional family of such systems. For a large class of families we argue that this topological invariant is an integer.</p>https://thesis.library.caltech.edu/id/eprint/14214From Building Blocks to Theories: EFThedron and a Haagerup TFT
https://resolver.caltech.edu/CaltechTHESIS:05262022-082058996
Authors: Huang, Tzu-Chen
Year: 2022
DOI: 10.7907/7yyr-rb39
<p>This thesis is dedicated to the study of certain building blocks of scattering amplitudes in (3+1)d Minkowskian spacetime and that of topological field theory in (1+1)d, together with the constraints which result from the properties of these building blocks.</p>
<p>The first part of the thesis is concerned with the introduction of an on-shell formalism for massless and massive particles. We identify all possible three-point tensor structures compatible with the little group symmetry and overall mass dimension, and use them to arrive at a new description of various scattering amplitudes through unitarity and locality. One of the objects that result from this construction, the spinning polynomial, is then fed into the dispersion relation to derive a convex hull constraining the EFT coefficients. We further investigate the intersection of the convex hull resulting from the positive expansion of residue and the half moment curve.</p>
<p>In the second part, we turn our attention to topological defect lines in (1+1)d topological field theory with Haagerup fusion ring. We first solve for the F-symbols of fusion categories in the Haagerup-Izumi family under the assumption of transparency. The purpose of transparency is twofold: it allows for a simple formula for F-symbols while at the same time tremendously simplifies the diagrammatic calculus with topological defect lines. Finally, we construct a topological field theory with 15 pointlike operators and demonstrate that it satisfies the four-point crossing constraints and torus one-point modular invariance constraints.</p>https://thesis.library.caltech.edu/id/eprint/14627