CaltechAUTHORS: Article
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A Caltech Library Repository Feedhttp://www.rssboard.org/rss-specificationpython-feedgenenFri, 02 Aug 2024 19:14:40 -0700Discrete and Continuum Approaches to Three-Dimensional Quantum Gravity
https://resolver.caltech.edu/CaltechAUTHORS:20161220-160613387
Year: 1991
DOI: 10.1142/S0217732391004140
It is shown that, in the three-dimensional lattice gravity defined by Ponzano and Regge, the space of physical states is isomorphic to the space of gauge-invariant functions on the moduli space of flat SU(2) connections over a two-dimensional surface, which gives physical states in the ISO(3) Chern–Simons gauge theory. To prove this, we employ the q-analogue of this model defined by Turaev and Viro as a regularization to sum over states. A recent work by Turaev suggests that the q-analogue model itself may be related to an Euclidean gravity with a cosmological constant proportional to 1/k^2, where q=e^(2πi/(k+2)).https://resolver.caltech.edu/CaltechAUTHORS:20161220-160613387Partition functions and topology-changing amplitudes in the three-dimensional lattice gravity of Ponzano and Regge
https://resolver.caltech.edu/CaltechAUTHORS:20161220-160213579
Year: 1992
DOI: 10.1016/0550-3213(92)90188-H
We define a physical Hilbert space for the three-dimensional lattice gravity of Ponzano and Regge and establish its isomorphism to the one in the ISO(3) Chern-Simons theory. It is shown that, for a handlebody of any genus, a Hartle-Hawking-type wave function of the lattice gravity transforms into the corresponding state in the Chern-Simons theory under this isomorphism. Using the Heegaard splitting of a three-dimensional manifold, the partition functions of each of these theories is expressed as an inner product of such wave functions. Since the isomorphism preserves the inner products, the partition functions of the two theories are the same for any closed orientable manifold. We also discuss a class of topology-changing amplitudes in the lattice gravity and their relation to the ones in the Chern-Simons theory.https://resolver.caltech.edu/CaltechAUTHORS:20161220-160213579Topological Lattice Models in Four Dimensions
https://resolver.caltech.edu/CaltechAUTHORS:20161220-155721883
Year: 1992
DOI: 10.1142/S0217732392004171
We define a lattice statistical model on a triangulated manifold in four dimensions associated to a group G. When G=SU(2), the statistical weight is constructed from the 15j-symbol as well as the 6j-symbol for recombination of angular momenta, and the model may be regarded as the four-dimensional version of the Ponzano-Regge model. We show that the partition function of the model is invariant under the Alexander moves of the simplicial complex, thus it depends only on the piecewise linear topology of the manifold. For an orientable manifold, the model is related to the so-called BF model. The q-analog of the model is also constructed, and it is argued that its partition function is invariant under the Alexander moves. It is discussed how to realize the 't Hooft operator in these models associated to a closed surface in four dimensions as well as the Wilson operator associated to a closed loop. Correlation functions of these operators in the q-deformed version of the model would define a new type of invariants of knots and links in four dimensions.https://resolver.caltech.edu/CaltechAUTHORS:20161220-155721883Schwinger-Dyson Equation in Three-Dimensional Simplicial Quantum Gravity
https://resolver.caltech.edu/CaltechAUTHORS:20161221-133310666
Year: 1993
DOI: 10.1143/ptp/89.1.1
We study the simplicial quantum gravity in three dimensions. Motivated by Boulatov's model which generates a sum over simplicial complexes weighted with the Turaev-Viro invariant, we introduce boundary operators in the simplicial gravity associated to compact orientable surfaces. An amplitude of the boundary operator is given by a sum over triangulations in the interior of the boundary surface. It turns out that the amplitude solves the Schwinger-Dyson equation even if we restrict the topology in the interior of the surface, as far as the surface is no-degenerate. We propose a set of factorization conditions on the amplitudes which singles out a solution associated to triangulations of S^3.https://resolver.caltech.edu/CaltechAUTHORS:20161221-133310666Holomorphic anomalies in topological field theories
https://resolver.caltech.edu/CaltechAUTHORS:20161220-154852744
Year: 1993
DOI: 10.1016/0550-3213(93)90548-4
We study the stringy genus-one partition function of N = 2 SCFTs. It is shown how to compute this using an anomaly in decoupling of BRST trivial states from the partition function. A particular limit of this partition function yields the partition function of topological theory coupled to topological gravity. As an application we compute the number of holomorphic elliptic curves over certain Calabi-Yau manifolds including the quintic threefold. This may be viewed as the first application of mirror symmetry at the string quantum level.https://resolver.caltech.edu/CaltechAUTHORS:20161220-154852744Kodaira-Spencer theory of gravity and exact results for quantum string amplitudes
https://resolver.caltech.edu/CaltechAUTHORS:20161221-125723575
Year: 1994
DOI: 10.1007/BF02099774
We develop techniques to compute higher loop string amplitudes for twisted N=2 theories with ĉ=3 (i.e. the critical case). An important ingredient is the discovery of an anomaly at every genus in decoupling of BRST trivial states, captured to all orders by a master anomaly equation. In a particular realization of the N=2 theories, the resulting string field theory is equivalent to a topological theory in six dimensions, the Kodaira-Spencer theory, which may be viewed as the closed string analog of the Chern-Simons theory. Using the mirror map this leads to computation of the 'number' of holomorphic curves of higher genus curves in Calabi-Yau manifolds. It is shown that topological amplitudes can also be reinterpreted as computing corrections to superpotential terms appearing in the effective 4d theory resulting from compactification of standard 10d superstrings on the corresponding N=2 theory. Relations with c=1 strings are also pointed out.https://resolver.caltech.edu/CaltechAUTHORS:20161221-125723575All loop N = 2 string amplitudes
https://resolver.caltech.edu/CaltechAUTHORS:20161220-154316012
Year: 1995
DOI: 10.1016/0550-3213(95)00365-Y
Using the N = 4 topological reformulation of N = 2 strings, we compute all loop partition function for special compactifications of N = 2 strings as a function of target moduli. We also reinterpret N = 4 topological amplitudes in terms of slightly modified N = 2 topological amplitudes. We present some preliminary evidence for the conjecture that N = 2 strings is the large N limit of Holomorphic Yang-Mills in four dimensions.https://resolver.caltech.edu/CaltechAUTHORS:20161220-154316012Two-dimensional black hole and singularities of CY manifolds
https://resolver.caltech.edu/CaltechAUTHORS:20161220-153626803
Year: 1996
DOI: 10.1016/0550-3213(96)00008-9
We study the degenerating limits of superconformal theories for compactifications on singular K3 and Calabi-Yau threefolds. We find that in both cases the degeneration involves creating an Euclidean two-dimensional black hole coupled weakly to the rest of the system. Moreover we find that the conformal theory of A_n singularities of K3 are the same as that of the symmetric fivebrane. We also find intriguing connections between ADE (1, n) non-critical strings and singular limits of superconformal theories on the corresponding ALE space.https://resolver.caltech.edu/CaltechAUTHORS:20161220-153626803D-branes on Calabi-Yau spaces and their mirrors
https://resolver.caltech.edu/CaltechAUTHORS:20161220-135624344
Year: 1996
DOI: 10.1016/0550-3213(96)00379-3
We study the boundary states of D-branes wrapped around supersymmetric cycles in a general Calabi-Yau manifold. In particular, we show how the geometric data on the cycles are encoded in the boundary states. As an application, we analyze how the mirror symmetry transforms D-branes, and we verify that it is consistent with the conjectured periodicity and the monodromy of the Ramond-Ramond field configuration on a Calabi-Yau manifold. This also enables us to study open string worldsheet instanton corrections and relate them to closed string instanton counting. The cases when the mirror symmetry is realized as T-duality are also discussed.https://resolver.caltech.edu/CaltechAUTHORS:20161220-135624344Summing up Dirichlet Instantons
https://resolver.caltech.edu/CaltechAUTHORS:20161221-111837116
Year: 1996
DOI: 10.1103/PhysRevLett.77.3296
We investigate quantum corrections to the moduli space for hypermultiplets for the type IIA string near a conifold singularity. We find a unique quantum deformation based on symmetry arguments which is consistent with a recent conjecture. The correction can be interpreted as an infinite sum coming from multiple wrappings of the Euclidean Dirichlet branes around the vanishing cycle.https://resolver.caltech.edu/CaltechAUTHORS:20161221-111837116Supersymmetric cycles in exceptional holonomy manifolds and Calabi-Yau four-folds
https://resolver.caltech.edu/CaltechAUTHORS:20161220-134740171
Year: 1996
DOI: 10.1016/S0550-3213(96)00491-9
We derive in the SCFT and low energy effective action frameworks the necessary and sufficient conditions for supersymmetric cycles in exceptional holonomy manifolds and Calabi-Yau four-folds. We show that the Cayley cycles in Spin(7) holonomy eight-manifolds and the associative and coassociative cycles in G2 holonomy seven-manifolds preserve half of the space-time supersymmetry. We find that while the holomorphic and special Lagrangian cycles in Calabi-Yau four-folds preserve half of the space-time supersymmetry, the Cayley submanifolds are novel as they preserve only one quarter of it. We present some simple examples. Finally, we discuss the implications of these supersymmetric cycles on mirror symmetry in higher dimensions.https://resolver.caltech.edu/CaltechAUTHORS:20161220-134740171D-brane actions on Kähler manifolds
https://resolver.caltech.edu/CaltechAUTHORS:20161221-131602093
Year: 1997
DOI: 10.4310/ATMP.1997.v1.n2.a3
We consider actions for N D-branes at points in a general Kähler manifold, which satisfy the axioms of D-geometry, and could be used as starting points for defining M(atrix)-theory in curved space. We show that the axioms cannot be satisfied unless the metric is Ricci flat, and argue that such actions do exist when the metric is Ricci flat. This may provide an argument for Ricci flatness in M(atrix)-theory.https://resolver.caltech.edu/CaltechAUTHORS:20161221-131602093Strong coupling dynamics of four-dimensional N = 1 gauge theories from M-theory fivebrane
https://resolver.caltech.edu/CaltechAUTHORS:20161221-131040211
Year: 1997
DOI: 10.4310/ATMP.1997.v1.n1.a1
It has been known that the fivebrane of type IIA theory can be used to give an exact low energy description of N=2 supersymmetric gauge theories in four dimensions. We follow the recent M theory description by Witten and show that it can be used to study theories with N=1 supersymmetry. The N=2 supersymmetry can be broken to N=1 by turning on a mass for the adjoint chiral superfield in the N=2 vector multiplet. We construct the configuration of the fivebrane for both finite and infinite values of the adjoint mass. The fivebrane describes strong coupling dynamics of N=1 theory with SU(N_c) gauge group and N_f quarks. For N_c > N_f, we show how the brane configuration encodes the information of the Affleck-Dine-Seiberg superpotential. For N_c = and < N_f, we study the deformation space of the brane configuration and compare it with the moduli space of the N=1 theory. We find agreement with field theory results, including the quantum deformation of the moduli space at N_c = N_f. We also prove the type II s-rule in M theory and find new non-renormalization theorems for N=1 superpotentials.https://resolver.caltech.edu/CaltechAUTHORS:20161221-131040211Mirror symmetry in three-dimensional gauge theories, quivers and D-branes
https://resolver.caltech.edu/CaltechAUTHORS:20161220-134318183
Year: 1997
DOI: 10.1016/S0550-3213(97)00125-9
We construct and analyze dual N = 4 supersymmetric gauge theories in three dimensions with unitary and symplectic gauge groups. The gauge groups and the field content of the theories are encoded in quiver diagrams. The duality exchanges the Coulomb and Higgs branches and the Fayet-Iliopoulos and mass parameters. We analyze the classical and the quantum moduli spaces of the theories and construct an explicit mirror map between the mass parameters and the Fayet-Iliopoulos parameters of the dual. The results generalize the relation between ALE spaces and moduli spaces of SU(n) and SO(2n) instantons. We interpret some of these results from the string theory viewpoint, for SU(n) by analyzing T-duality and extremal transitions in type II string compactifications, for SO(2n) by using D-branes as probes. Finally, we make a proposal for the moduli space of vacua of these theories in the absence of matter.https://resolver.caltech.edu/CaltechAUTHORS:20161220-134318183Mirror symmetry in three-dimensional gauge theories, SL(2,Z) and D-brane moduli spaces
https://resolver.caltech.edu/CaltechAUTHORS:20161220-133645222
Year: 1997
DOI: 10.1016/S0550-3213(97)00115-6
We construct intersecting D-brane configurations that encode the gauge groups and field content of dual N = 4 supersymmetric gauge theories in three dimensions. The duality which exchanges the Coulomb and Higgs branches and the Fayet-Iliopoulos and mass parameters is derived from the SL (2, Z) symmetry of the type IIB string. Using the D-brane configurations we construct explicitly this mirror map between the dual theories and study the instanton corrections in the D-brane world-volume theory via open string instantons. A general procedure to obtain mirror pairs is presented and illustrated. We encounter transitions among different field theories that correspond to smooth movements in the D-brane moduli space. We discuss the relation between the duality of the gauge theories and the level-rank duality of affine Lie algebras. Examples of other dual theories are presented and explained via T-duality and extremal transitions in type II string compactifications. Finally we discuss a second way to study instanton corrections in the gauge theory, by wrapping 5-branes around six-cycles in M-theory compactified on a Calabi-Yau 4-fold.https://resolver.caltech.edu/CaltechAUTHORS:20161220-133645222Issues in M(atrix) theory compactification
https://resolver.caltech.edu/CaltechAUTHORS:20161220-131914782
Year: 1997
DOI: 10.1016/S0370-2693(97)00424-3
We discuss issues concerning M(atrix) theory compactifications on curved spaces. We argue from the form of the graviton propagator on curved space that excited string states do not decouple from the annulus D0-brane υ^4 amplitude, unlike the flat space case. This argurment shows that a large class of quantum mechanical systems with a finite number of degrees of freedom cannot reproduce supergravity answers. We discuss the specific example of an ALE space and suggest sources of possible higher derivative terms that might help reproduce supergravity results.https://resolver.caltech.edu/CaltechAUTHORS:20161220-131914782Geometry of N = 1 dualities in four dimensions
https://resolver.caltech.edu/CaltechAUTHORS:20161220-132709721
Year: 1997
DOI: 10.1016/S0550-3213(97)00304-0
We discuss how N = 1 dualities in four dimensions are geometrically realized by wrapping D-branes about 3-cycles of Calabi-Yau threefolds. In this setup the N = 1 dualities for SU, SO and USp gauge groups with fundamental fields get mapped to statements about the monodromy and relations among 3-cycles of Calabi-Yau threefolds. The connection between the theory and its dual requires passing through configurations which are T-dual to the well-known phenomenon of decay of BPS states in N = 2 field theories in four dimensions. We compare our approach to recent works based on configurations of D-branes in the presence of NS 5-branes and give simple classical geometric derivations of various exotic dynamics involving D-branes ending on NS branes.https://resolver.caltech.edu/CaltechAUTHORS:20161220-132709721Non-Abelian conifold transitions and N = 4 dualities in three dimensions
https://resolver.caltech.edu/CaltechAUTHORS:20161220-131259376
Year: 1997
DOI: 10.1016/S0550-3213(97)00529-4
We show how the Higgs mechanism for non-Abelian N = 2 gauge theories in four dimensions is geometrically realized in the context of type II strings as transitions among compactifications of Calabi-Yau 3-folds. We use this result and T-duality of a further compactification on a circle to derive N = 4, d = 3 dual field theories. This reduces the dualities for N = 4 gauge systems in three dimensions to perturbative symmetries of string theory. Moreover, we find that the dual of a gauge system always exists but may or may not correspond to a Lagrangian system. In particular, we verify a conjecture of Intriligator and Seiberg that an ordinary gauge system is dual to compactification of exceptional tensionless string theory down to three dimensions.https://resolver.caltech.edu/CaltechAUTHORS:20161220-131259376Why matrix theory is hard
https://resolver.caltech.edu/CaltechAUTHORS:20161221-124148504
Year: 1998
DOI: 10.1016/S0370-2693(98)00114-2
Recently Sen and Seiberg gave a prescription for constructing the matrix theory in any superstring background. We use their prescription to test the finite N matrix theory conjecture on an ALE space. Based on our earlier work with Shenker, we find a sharper discrepancy between matrix theory computation and supergravity prediction. We discuss subtleties in the light-front quantization which may lead to a resolution to the discrepancy.https://resolver.caltech.edu/CaltechAUTHORS:20161221-124148504Kähler potential and higher derivative terms from M-theory fivebrane
https://resolver.caltech.edu/CaltechAUTHORS:20161220-125221606
Year: 1998
DOI: 10.1016/S0550-3213(98)00152-7
The construction of four-dimensional supersymmetric gauge theories via the fivebrane of M-theory wrapped around a Riemann surface has been successfully applied to the computation of holomorphic quantities of field theory. In this paper we compute non-holomorphic quantities in the eleven-dimensional supergravity limit of M-theory. While the Kähler potential on the Coulomb of N = 2 theories is correctly reproduced, higher derivative terms in the N = 2 effective action differ from what is expected for the four-dimensional gauge theory. For the Kähler potential of N = 1 theories at an abelian Coulomb phase, the result again differs from what is expected for the four-dimensional gauge theory. Using a gravitational back-reaction method for the fivebrane we compute the metric on the Higgs branch of N = 2 gauge theories. Here we find an agreement with the results expected for the gauge theories. A similar computation of the metric on N = 1 Higgs branches yields information on the complex structure associated with the flavor rotation in one case and the classical metric in another. We discuss what four-dimensional field theory quantities can be computed via the fivebrane in the supergravity limit of M-theory.https://resolver.caltech.edu/CaltechAUTHORS:20161220-125221606Spectrum of Large N Gauge Theory from Supergravity
https://resolver.caltech.edu/CaltechAUTHORS:20161221-111157185
Year: 1998
DOI: 10.1103/PhysRevLett.80.4116
Recently, Maldacena proposed that the large N limit of the N=4 supersymmetric gauge theory in four dimensions with U(N) gauge group is dual to the type IIB superstring theory on AdS_5 ×S^5. We use this proposal to study the spectrum of the large N gauge theory on R×S^3 in a low energy regime. We find that the spectrum is discrete and evenly spaced, and the number of states at each energy level is smaller than the one predicted by the naive extrapolation of the Bekenstein-Hawking formula to the low energy regime. We also show that the gauge theory describes a region of spacetime behind the horizon as well as the region in front.https://resolver.caltech.edu/CaltechAUTHORS:20161221-111157185Branes and dynamical supersymmetry breaking
https://resolver.caltech.edu/CaltechAUTHORS:20161220-124550810
Year: 1998
DOI: 10.1016/S0550-3213(98)00252-1
We study dynamical supersymmetry breaking in four dimensions using the fivebrane of M theory, in particular for the Izawa-Yanagida-Intriligator-Thomas (IYIT) model, which we realize as the worldvolume theory of a certain M theory fivebrane configuration. From the brane point of view, supersymmetry is broken when a holomorphic configuration with the proper boundary conditions does not exist. We discuss the difference between explicit and spontaneous supersymmetry breaking and between runaway behavior and having a stable vacuum. As a preparation for the study of the IYIT model, we examine a realization of the orientifold four-plane in M theory. We derive known as well as new results on the moduli spaces of N = 2 and N = 1 theories with symplectic gauge groups. These results are based on a hypothesis that a certain intersection of the fivebrane and the Z_2 fixed plane breaks supersymmetry. In the IYIT model, we show that the brane exhibits runaway behavior when the flavor group is gauged. On the other hand, if the flavor group is not gauged, we find that the brane does not run away. We suggest that a stable supersymmetry-breaking vacuum is realized in the region beyond the reach of the supergravity approximation.https://resolver.caltech.edu/CaltechAUTHORS:20161220-124550810Membrane scattering in curved space with M-momentum transfer
https://resolver.caltech.edu/CaltechAUTHORS:20161220-123933919
Year: 1998
DOI: 10.1016/S0550-3213(98)00253-3
We study membrane scattering in a curved space with non-zero M-momentum p11 transfer. In the low-energy short-distance region, the membrane dynamics is described by a three-dimensional N = 4 supersymmetric gauge theory. We study an n-instanton process of the gauge theory, corresponding to the exchange of n units of p11, and compare the result with the scattering amplitude computed in the low-energy long-distance region using supergravity. We find that they behave differently. We show that this result is not in contradiction with the large-N Matrix Theory conjecture, by pointing out that cutoff scales of the supergravity and the gauge theory are complementary to each other.https://resolver.caltech.edu/CaltechAUTHORS:20161220-123933919M theory fivebrane and SQCD
https://resolver.caltech.edu/CaltechAUTHORS:20161220-130418424
Year: 1998
DOI: 10.1016/S0920-5632(98)00142-X
A low energy effective theory of parallel D(irichlet) branes is a gauge theory with sixteen supercharges, but one can consider a web of brane to realize situations with reduced number of supersymmetry [1]. In this talk, I will discuss four-dimensional theories with N = 1 and 2 supersymmetry (i.e. four and eight supercharges). In the case of theories with N = 2 supersymmetry, the exact description of the Coulomb branch is given by reinterpreting the web of branes as a configuration of a single fivebrane in the IIA theory [2,3]. Recently we studied the case with N = 1 supersymmetry, and found that description in term of the fivebrane in M Theory captures strong coupling dynamics of the N = 1 gauge theory in four dimensions [4]. In particular, we found that the configuration of the fivebrane geometrically encodes information on the Affleck-Dine-Seiberg superpotential and the structure of the quantum moduli space of vacua. Simultaneously to our work, the case without matter field was studied in [5]. A related work also appeared in [6].https://resolver.caltech.edu/CaltechAUTHORS:20161220-130418424On the field theory limit of D-instantons
https://resolver.caltech.edu/CaltechAUTHORS:OOGjhep98
Year: 1998
DOI: 10.1088/1126-6708/1998/11/013
We study the dilaton/axion configuration near D-instantons in type IIB superstring theory. In the field theory limit, the metric near the instantons becomes flat in the string frame as well as in the Einstein frame. In the large N limit, the string coupling constant becomes zero except near the origin. The supersymmetry of this configuration is analyzed. An implication of this result to the IIB Matrix Model is discussed.https://resolver.caltech.edu/CaltechAUTHORS:OOGjhep98Aspects of large N gauge theory dynamics as seen by string theory
https://resolver.caltech.edu/CaltechAUTHORS:20161221-104619580
Year: 1998
DOI: 10.1103/PhysRevD.58.106002
In this paper we explore some of the features of large N supersymmetric and nonsupersymmetric gauge theories using Maldacena's duality conjectures. We show that the resulting strong coupling behavior of the gauge theories is consistent with our qualitative expectations of these theories. Some of these consistency checks are highly nontrivial and give additional evidence for the validity of the proposed dualities.https://resolver.caltech.edu/CaltechAUTHORS:20161221-104619580String theory on AdS_3
https://resolver.caltech.edu/CaltechAUTHORS:20090918-132530709
Year: 1998
DOI: 10.1088/1126-6708/1998/12/026
It was shown by Brown and Henneaux that the classical theory of gravity on AdS_3 has an infinite-dimensional symmetry group forming a Virasoro algebra. More recently, Giveon, Kutasov and Seiberg (GKS) constructed the corresponding Virasoro generators in the first-quantized string theory on AdS_3. In this paper, we explore various aspects of string theory on AdS_3 and study the relation between these two works. We show how semi-classical properties of the string theory reproduce many features of the AdS/CFT duality. Furthermore, we examine how the Virasoro symmetry of Brown and Henneaux is realized in string theory, and show how it leads to the Virasoro Ward identities of the boundary CFT. The Virasoro generators of GKS emerge naturally in this analysis. Our work clarifies several aspects of the GKS construction: why the Brown-Henneaux Virasoro algebra can be realized on the first-quantized Hilbert space, to what extent the free-field approximation is valid, and why the Virasoro generators act on the string worldsheet localized near the boundary of AdS_3. On the other hand, we find that the way the central charge of the Virasoro algebra is generated is different from the mechanism proposed by GKS.https://resolver.caltech.edu/CaltechAUTHORS:20090918-132530709Glueball mass spectrum from supergravity
https://resolver.caltech.edu/CaltechAUTHORS:CSAjhep99
Year: 1999
DOI: 10.1088/1126-6708/1999/01/017
We calculate the spectrum of glueball masses in non-supersymmetric Yang-Mills theory in three and four dimensions, based on a conjectured duality between supergravity and large N gauge theories. The glueball masses are obtained by solving supergravity wave equations in a black hole geometry. We find that the mass ratios are in good numerical agreement with the available lattice data. We also compute the leading (g^2_(YM)N)^(−1) corrections to the glueball masses, by taking into account stringy corrections to the supergravity action and to the black hole metric. We find that the corrections to the masses are negative and of order (g^2_(YM)N)^(−3/2). Thus for a fixed ultraviolet cutoff the masses decrease as we decrease the 't Hooft coupling, in accordance with our expectation about the continuum limit of the gauge theories.https://resolver.caltech.edu/CaltechAUTHORS:CSAjhep99Wilson Loops and Minimal Surfaces
https://resolver.caltech.edu/CaltechAUTHORS:20161220-074236256
Year: 1999
DOI: 10.1103/PhysRevD.60.125006
The AdS/CFT correspondence suggests that the Wilson loop of the large N gauge theory with N=4 supersymmetry in 4 dimensions is described by a minimal surface in AdS_5 x S^5. We examine various aspects of this proposal, comparing gauge theory expectations with computations of minimal surfaces. There is a distinguished class of loops, which we call BPS loops, whose expectation values are free from ultra-violet divergence. We formulate the loop equation for such loops. To the extent that we have checked, the minimal surface in AdS_5 x S^5 gives a solution of the equation. We also discuss the zig-zag symmetry of the loop operator. In the N=4 gauge theory, we expect the zig-zag symmetry to hold when the loop does not couple the scalar fields in the supermultiplet. We will show how this is realized for the minimal surface.https://resolver.caltech.edu/CaltechAUTHORS:20161220-074236256Large N Field Theories, String Theory and Gravity
https://resolver.caltech.edu/CaltechAUTHORS:20161219-110810298
Year: 2000
DOI: 10.1016/S0370-1573(99)00083-6
We review the holographic correspondence between field theories and string/M theory, focusing on the relation between compactifications of string/M theory on Anti-de Sitter spaces and conformal field theories. We review the background for this correspondence and discuss its motivations and the evidence for its correctness. We describe the main results that have been derived from the correspondence in the regime that the field theory is approximated by classical or semiclassical gravity. We focus on the case of the N=4 supersymmetric gauge theory in four dimensions, but we discuss also field theories in other dimensions, conformal and non-conformal, with or without supersymmetry, and in particular the relation to QCD. We also discuss some implications for black hole physics.https://resolver.caltech.edu/CaltechAUTHORS:20161219-110810298Wilson loops in large-N theories
https://resolver.caltech.edu/CaltechAUTHORS:OOGcqg00
Year: 2000
DOI: 10.1088/0264-9381/17/5/331
We discuss how various aspects of Wilson loops in large-N gauge theories are studied from the point of view of the AdS-CFT correspondence.https://resolver.caltech.edu/CaltechAUTHORS:OOGcqg00Gauge Theory and String Theory; An Introduction to the AdS/CFT Correspondence
https://resolver.caltech.edu/CaltechAUTHORS:20161219-105646214
Year: 2000
DOI: 10.1016/S0920-5632(00)91597-4
In this talk, I would like to show you some of the recent developments in superstring theory, in particular the relation between gauge theory and string theory. String theory was originally invented as a theory of hadrons, but it was superseded by the gauge theory. It then found its employment in quantum gravity. Now it seems that string theory and gauge theory are meeting again, and I hope this new direction will provide an interesting arena where lattice gauge theorists and string theorists can interact and exchange ideas, benefiting both.https://resolver.caltech.edu/CaltechAUTHORS:20161219-105646214Knot Invariants and Topological Strings
https://resolver.caltech.edu/CaltechAUTHORS:20161219-085922769
Year: 2000
DOI: 10.1016/S0550-3213(00)00118-8
We find further evidence for the conjecture relating large N Chern-Simons theory on S^3 with topological string on the resolved conifold geometry by showing that the Wilson loop observable of a simple knot on S³ (for any representation) agrees to all orders in N with the corresponding quantity on the topological string side. For a general knot, we find a reformulation of the knot invariant in terms of new integral invariants, which capture the spectrum (and spin) of M2 branes ending on M5 branes embedded in the resolved conifold geometry. We also find an intriguing link between knot invariants and superpotential terms generated by worldsheet instantons in N=1 supersymmetric theories in 4 dimensions.https://resolver.caltech.edu/CaltechAUTHORS:20161219-085922769Holography in superspace
https://resolver.caltech.edu/CaltechAUTHORS:OOGjhep00
Year: 2000
DOI: 10.1088/1126-6708/2000/07/045
The AdS/CFT correspondence identifies the coordinates of the conformal boundary of anti-de Sitter space with the coordinates of the conformal field theory. We generalize this identification to theories formulated in superspace. As an application of our results, we study a class of Wilson loops in Script N = 4 super-Yang-Mills theory. A gauge theory computation shows that the expectation values of these loops are invariant under a local κ-symmetry, except at intersections. We identify this with the κ-invariance of the associated string worldsheets in the corresponding bulk superspace.https://resolver.caltech.edu/CaltechAUTHORS:OOGjhep00Nonrelativistic closed string theory
https://resolver.caltech.edu/CaltechAUTHORS:GOMjmp01
Year: 2001
DOI: 10.1063/1.1372697
We construct a Galilean invariant nongravitational closed string theory whose excitations satisfy a nonrelativistic dispersion relation. This theory can be obtained by taking a consistent low energy limit of any of the conventional string theories, including the heterotic string. We give a finite first order worldsheet Hamiltonian for this theory and show that this string theory has a sensible perturbative expansion, interesting high energy behavior of scattering amplitudes and a Hagedorn transition of the thermal ensemble. The strong coupling duals of the Galilean superstring theories are considered and are shown to be described by an eleven-dimensional Galilean invariant theory of light membrane fluctuations. A new class of Galilean invariant nongravitational theories of light-brane excitations are obtained. We exhibit dual formulations of the strong coupling limits of these Galilean invariant theories and show that they exhibit many of the conventional dualities of M theory in a nonrelativistic setting.https://resolver.caltech.edu/CaltechAUTHORS:GOMjmp01Strings in AdS3 and the SL(2,R) WZW model. II: Euclidean black hole
https://resolver.caltech.edu/CaltechAUTHORS:MALjmp01b
Year: 2001
DOI: 10.1063/1.1377039
We consider the one-loop partition function for Euclidean BTZ black hole back-grounds or equivalently thermal AdS3 backgrounds which are quotients of H3 (Euclidean AdS3). The one-loop partition function is modular invariant and we can read off the spectrum which is consistent to that found in hep-th/0001053. We see long strings and discrete states in agreement with the expectations.https://resolver.caltech.edu/CaltechAUTHORS:MALjmp01bStrings in AdS3 and the SL(2,R) WZW model. I: The spectrum
https://resolver.caltech.edu/CaltechAUTHORS:MALjmp01a
Year: 2001
DOI: 10.1063/1.1377273
In this paper we study the spectrum of bosonic string theory on AdS3. We study classical solutions of the SL(2,R) WZW model, including solutions for long strings with nonzero winding number. We show that the model has a symmetry relating string configurations with different winding numbers. We then study the Hilbert space of the WZW model, including all states related by the above symmetry. This leads to a precise description of long strings. We prove a no-ghost theorem for all the representations that are involved and discuss the scattering of the long string.https://resolver.caltech.edu/CaltechAUTHORS:MALjmp01aHolography and Defect Conformal Field Theories
https://resolver.caltech.edu/CaltechAUTHORS:20161220-101329666
Year: 2001
DOI: 10.48550/arXiv.0111135
We develop both the gravity and field theory sides of the Karch-Randall conjecture that the near-horizon description of a certain D5-D3 brane configuration in string theory, realized as AdS_5 x S^5 bisected by an AdS_4 x S^2 "brane", is dual to N=4 Super Yang-Mills theory in R^4 coupled to an R^3 defect. We propose a complete Lagrangian for the field theory dual, a novel "defect superconformal field theory" wherein a subset of the fields of N=4 SYM interacts with a d=3 SU(N) fundamental hypermultiplet on the defect preserving conformal invariance and 8 supercharges. The Kaluza-Klein reduction of wrapped D5 modes on AdS_4 x S^2 leads to towers of short representations of OSp(4|4), and we construct the map to a set of dual gauge-invariant defect operators O_3 possessing integer conformal dimensions. Gravity calculations of and are given. Spacetime and N-dependence matches expectations from dCFT, while the behavior as functions of λ = g^2 N at strong and weak coupling is generically different. We comment on a class of correlators for which a non-renormalization theorem may still exist. Partial evidence for the conformality of the quantum theory is given, including a complete argument for the special case of a U(1) gauge group. Some weak coupling arguments which illuminate the duality are presented.https://resolver.caltech.edu/CaltechAUTHORS:20161220-101329666Exact solution to the Seiberg-Witten equation of noncommutative gauge theory
https://resolver.caltech.edu/CaltechAUTHORS:OKAprd01
Year: 2001
DOI: 10.1103/PhysRevD.64.046009
We derive an exact expression for the Seiberg-Witten map of noncommutative gauge theory. It is found by studying the coupling of the gauge field to the Ramond-Ramond potentials in string theory. Our result also proves the earlier conjecture by Liu.https://resolver.caltech.edu/CaltechAUTHORS:OKAprd01Open Strings on AdS₂ Branes
https://resolver.caltech.edu/CaltechAUTHORS:20111104-094701527
Year: 2001
DOI: 10.1016/S0550-3213(01)00333-9
We study the spectrum of open strings on AdS₂ branes in AdS₃ in an NS-NS background, using the SL(2,R) WZW model. When the brane carries no fundamental string charge, the
open string spectrum is the holomorphic square root of the spectrum of closed strings in AdS₃. It contains short and long strings, and is invariant under spectral flow. When the
brane carries fundamental string charge, the open string spectrum again contains short and long strings in all winding sectors. However, branes with fundamental string charge break half the spectral flow symmetry. This has different implications for short and long strings. As the fundamental string charge increases, the brane approaches the boundary of AdS₃. In this limit, the induced electric field on the worldvolume reaches its critical value, producing noncommutative open string theory on AdS₂.https://resolver.caltech.edu/CaltechAUTHORS:20111104-094701527Seiberg-Witten transforms of noncommutative solitons
https://resolver.caltech.edu/CaltechAUTHORS:HASprd01
Year: 2001
DOI: 10.1103/PhysRevD.64.106005
We evaluate the Seiberg-Witten map for solitons and instantons in noncommutative gauge theories in various dimensions. We show that solitons constructed using the projection operators have delta-function supports when expressed in the commutative variables. This gives a precise identification of the moduli of these solutions as locations of branes. On the other hand, an instanton solution in four dimensions allows deformation away from the projection operator construction. We evaluate the Seiberg-Witten transform of the U(2) instanton and show that it has a finite size determined by the noncommutative scale and by the deformation parameter ρ. For large ρ, the profile of the D0-brane density of the instanton agrees surprisingly well with that of the Belavin-Polyakov-Schwarz-Tyupkin (BPST) instanton on commutative space.https://resolver.caltech.edu/CaltechAUTHORS:HASprd01Strings in AdS3 and the SL(2,R) WZW model. III. Correlation functions
https://resolver.caltech.edu/CaltechAUTHORS:MALprd02
Year: 2002
DOI: 10.1103/PhysRevD.65.106006
We consider correlation functions for string theory on AdS3. We analyze their singularities and we provide a physical interpretation for them. We explain which worldsheet correlation functions have a sensible physical interpretation in terms of the boundary theory. We consider the operator product expansion of the four-point function and we find that it factorizes only if a certain condition is obeyed. We explain that this is the correct physical result. We compute correlation functions involving spectral flowed operators and we derive a constraint on the amount of winding violation.https://resolver.caltech.edu/CaltechAUTHORS:MALprd02Permeable conformal walls and holography
https://resolver.caltech.edu/CaltechAUTHORS:BACjhep02
Year: 2002
DOI: 10.1088/1126-6708/2002/06/027
We study conformal field theories in two dimensions separated by domain walls, which preserve at least one Virasoro algebra. We develop tools to study such domain walls, extending and clarifying the concept of `folding' discussed in the condensed-matter literature. We analyze the conditions for unbroken supersymmetry, and discuss the holographic duals in AdS3 when they exist. One of the interesting observables is the Casimir energy between a wall and an anti-wall. When these separate free scalar field theories with different target-space radii, the Casimir energy is given by the dilogarithm function of the reflection probability. The walls with holographic duals in AdS3 separate two sigma models, whose target spaces are moduli spaces of Yang-Mills instantons on T4 or K3. In the supergravity limit, the Casimir energy is computable as classical energy of a brane that connects the walls through AdS3. We compare this result with expectations from the sigma-model point of view.https://resolver.caltech.edu/CaltechAUTHORS:BACjhep02Boundary States for AdS₂ Branes in AdS₃
https://resolver.caltech.edu/CaltechAUTHORS:20111019-133017114
Year: 2002
DOI: 10.1016/S0550-3213(02)00239-0
We construct boundary states for the AdS₂ D-branes in AdS₃. We show that, in the semi-classical limit, the boundary states correctly reproduce geometric configurations of these branes. We use the boundary states to compute the one loop free energy of open string stretched between the branes. The result agrees precisely with the open string computation in hep-th/0106129.https://resolver.caltech.edu/CaltechAUTHORS:20111019-133017114Penrose Limit of N = 1 Gauge Theories
https://resolver.caltech.edu/CaltechAUTHORS:20111102-095258870
Year: 2002
DOI: 10.1016/S0550-3213(02)00396-6
We find a Penrose limit of AdS_5 × T^(1,1) which gives the pp-wave geometry identical to the one that appears in the Penrose limit of AdS_5 × S^5. This leads us to conjecture
that there is a subsector of the corresponding N = 1 gauge theory which has enhanced N = 4 supersymmetry. We identify operators in the N = 1 gauge theory with stringy
excitations in the pp-wave geometry and discuss how the gauge theory operators fall into N = 4 supersymmetry multiplets. We find similar enhancement of symmetry in some other models, but there are also examples in which there is no supersymmetry enhancement in the Penrose limit.https://resolver.caltech.edu/CaltechAUTHORS:20111102-095258870Worldsheet derivation of a large N duality
https://resolver.caltech.edu/CaltechAUTHORS:OOGnpb02
Year: 2002
DOI: 10.1016/S0550-3213(02)00620-X
We give a worldsheet proof of the equivalence between the U(N) Chern–Simons gauge theory on S³ and the topological closed string theory on the resolved conifold geometry. When the 't Hooft coupling of the gauge theory is small, the dual closed string worldsheet develops a new branch. We show that the fluctuations of the worldsheet into this branch effectively correspond to "holes" on the worldsheet, generating an open string sector. This leads to a microscopic description of how the 't Hooft expansion of gauge theory amplitudes is reproduced in the closed string computation. We find that the closed string amplitudes also contain terms which are not captured in the 't Hooft expansion but are present in the exact computation in the gauge theory amplitudes. These arise when the whole Riemann surface is in the new branch. We also discuss the cases with SO and Sp gauge groups.https://resolver.caltech.edu/CaltechAUTHORS:OOGnpb02The C-deformation of gluino and non-planar diagrams
https://resolver.caltech.edu/CaltechAUTHORS:OOGatmp03a
Year: 2003
DOI: 10.48550/arXiv.0302109
We consider a deformation of N = 1 supersymmetric gauge theories in four dimensions, which we call the C-deformation, where the gluino field satisfies a Clifford-like algebra dictated by a self-dual two-form, instead of the standard Grassmannian algebra. The superpotential of the deformed gauge theory is computed by the full partition function of an associated matrix model (or more generally a bosonic gauge theory), including non-planar diagrams. In this identification, the strength of the two-form controls the genus expansion of the matrix model partition function. For the case of pure N = 1 Yang-Mills this deformation leads to the identification of the all genus partition function of c non-critical bosonic string at self-dual radius as the glueball superpotential. Though the C-deformation violates Lorentz invariance, the deformed F-terms are Lorentz invariant and the Lorentz violation is screened in the IR.https://resolver.caltech.edu/CaltechAUTHORS:OOGatmp03aGravity Induced C-Deformation
https://resolver.caltech.edu/CaltechAUTHORS:OOGatmp03b
Year: 2003
DOI: 10.48550/arXiv.0303063
We study F-terms describing coupling of the supergravity to N = 1 supersymmetric gauge theories which admit large N expansions. We show that these F-terms are given by summing over genus one non-planar diagrams of the large N expansion of the associated matrix model (or more generally bosonic gauge theory). The key ingredient in this derivation is the observation that the chiral ring of the gluino fields is deformed by the supergravity fields, generalizing the C-deformation which was recently introduced. The gravity induced part of the C-deformation can be derived from the Bianchi identities of the supergravity, but understanding gravitational corrections to the F-terms requires a non-traditional interpretation of these identities.https://resolver.caltech.edu/CaltechAUTHORS:OOGatmp03bInside the horizon with AdS/CFT
https://resolver.caltech.edu/CaltechAUTHORS:KRAprd03
Year: 2003
DOI: 10.1103/PhysRevD.67.124022
Using the eternal BTZ black hole as a concrete example, we show how spacelike singularities and horizons can be described in terms of AdS/CFT amplitudes. Our approach is based on analytically continuing amplitudes defined in a Euclidean signature. This procedure yields finite Lorentzian amplitudes. The naive divergences associated with the Milne type singularity of BTZ black holes are regulated by an iepsilon prescription inherent in the analytic continuation and a cancellation between future and past singularities. The boundary description corresponds to a tensor product of two CFTs in an entangled state, as in previous work. We give two bulk descriptions corresponding to two different analytic continuations. In the first, only regions outside the horizon appear explicitly, and so amplitudes are manifestly finite. In the second, regions behind the horizon and on both sides of the singularity appear, thus yielding finite amplitudes for virtual particles propagating through the black hole singularity. This equivalence between descriptions only outside and both inside and outside the horizon is reminiscent of the ideas of black hole complementarity.https://resolver.caltech.edu/CaltechAUTHORS:KRAprd03Quantum aspects of the Seiberg–Witten map in noncommutative Chern–Simons theory
https://resolver.caltech.edu/CaltechAUTHORS:20111011-075425541
Year: 2003
DOI: 10.1016/S0550-3213(03)00383-3
Noncommutative Chern–Simons theory can be classically mapped to commutative Chern–Simons theory by the Seiberg–Witten map. We provide evidence that the equivalence persists at the quantum level by computing two and three-point functions of field strengths on the commutative side and their Seiberg–Witten transforms on the noncommutative side to the first nontrivial order in perturbation theory.https://resolver.caltech.edu/CaltechAUTHORS:20111011-075425541Planar gravitational corrections for supersymmetric
gauge theories
https://resolver.caltech.edu/CaltechAUTHORS:DIJjhep04
Year: 2004
DOI: 10.1088/1126-6708/2004/04/028
In this paper we discuss the contribution of planar diagrams to gravitational F-terms for N = 1 supersymmetric gauge theories admitting large N description. We show how the planar diagrams lead to a universal contribution at the extremum of the glueball superpotential, leaving only the genus one contributions, as was previously conjectured. We also discuss the physical meaning of gravitational F-terms.https://resolver.caltech.edu/CaltechAUTHORS:DIJjhep04S-duality and topological strings
https://resolver.caltech.edu/CaltechAUTHORS:NEKjhep04
Year: 2004
DOI: 10.1088/1126-6708/2004/10/009
In this paper we show how S-duality of type-IIB superstrings leads to an S-duality relating A- and B-model topological strings on the same Calabi-Yau as had been conjectured recently: D-instantons of the B-model correspond to A-model perturbative amplitudes and D-instantons of the A-model capture perturbative B-model amplitudes. Moreover this confirms the existence of new branes in the two models. As an application we explain the recent results concerning A-model topological strings on Calabi-Yau and its equivalence to the statistical mechanical model of melting crystal.https://resolver.caltech.edu/CaltechAUTHORS:NEKjhep04D-branes and phases on string worldsheet
https://resolver.caltech.edu/CaltechAUTHORS:OKUnpb04
Year: 2004
DOI: 10.1016/j.nuclphysb.2004.08.036
We generalize the worldsheet derivation of the topological open/closed string duality given in hep-th/0205297 to cases when there are different types of D-branes on the open string side. We use the mirror Landau–Ginzburg description to clarify the correspondence between D-branes on the open string side and C phases on the closed string side. We also discuss the duality from the point of view of the B-model.https://resolver.caltech.edu/CaltechAUTHORS:OKUnpb04Black hole attractors and the topological string
https://resolver.caltech.edu/CaltechAUTHORS:OOGprd04.931
Year: 2004
DOI: 10.1103/PhysRevD.70.106007
A simple relationship of the form ZBH = |Ztop|2 is conjectured, where ZBH is a supersymmetric partition function for a four-dimensional BPS black hole in a Calabi-Yau compactification of Type II superstring theory and Ztop is a second-quantized topological string partition function evaluated at the attractor point in moduli space associated to the black hole charges. Evidence for the conjecture in a perturbation expansion about large graviphoton charge is given. The microcanonical ensemble of BPS black holes can be viewed as the Wigner function associated to the wave function defined by the topological string partition function.https://resolver.caltech.edu/CaltechAUTHORS:OOGprd04.931On the Worldsheet Derivation of Large N Dualities for the Superstring
https://resolver.caltech.edu/CaltechAUTHORS:20110817-084105266
Year: 2004
DOI: 10.1007/s00220-004-1181-9
Large N topological string dualities have led to a class of proposed open/closed dualities for superstrings. In the topological string context, the worldsheet derivation of these dualities has already been given. In this paper we take the first step in deriving the full ten-dimensional superstring dualities by showing how the dualities arise on the superstring worldsheet at the level of F terms. As part of this derivation, we show for F-term computations that the hybrid formalism for the superstring is equivalent to a ĉ=5 topological string in ten-dimensional spacetime. Using the ĉ=5 description, we then show that the D brane boundary state for the ten-dimensional open superstring naturally emerges on the worldsheet of the closed superstring dual.https://resolver.caltech.edu/CaltechAUTHORS:20110817-084105266Black holes, q-deformed 2d Yang-Mills, and non-perturbative topological strings
https://resolver.caltech.edu/CaltechAUTHORS:20110513-093141123
Year: 2005
DOI: 10.1016/j.nuclphysb.2005.02.035
We count the number of bound states of BPS black holes on local Calabi–Yau three-folds involving a Riemann surface of genus g. We show that the corresponding gauge theory on the brane reduces to a q-deformed Yang–Mills theory on the Riemann surface. Following the recent connection between the black hole entropy and the topological string partition function, we find that for a large black hole charge N, up to corrections of O(e^(−N)), ZBH is given as a sum of a square of chiral blocks, each of which corresponds to a specific D-brane amplitude. The leading chiral block, the vacuum block, corresponds to the closed topological string amplitudes. The subleading chiral blocks involve topological string amplitudes with D-brane insertions at (2g−2) points on the Riemann surface analogous to the Ω points in the large N 2d Yang–Mills theory. The finite N amplitude provides a non-perturbative definition of topological strings in these backgrounds. This also leads to a novel non-perturbative formulation of c=1 non-critical string at the self-dual radius.https://resolver.caltech.edu/CaltechAUTHORS:20110513-093141123Hartle-Hawking Wave-Function for Flux Compactifications: the Entropic Principle
https://resolver.caltech.edu/CaltechAUTHORS:20190927-133504041
Year: 2005
DOI: 10.1007/s11005-005-0022-x
We argue that the topological string partition function, which has been known to correspond to a wave-function, can be interpreted as an exact "wave-function of the universe" in the mini-superspace sector of physical superstring theory. This realizes the idea of Hartle and Hawking in the context of string theory, including all loop quantum corrections. The mini-superspace approximation is justified as an exact description of BPS quantities. Moreover this proposal leads to a conceptual explanation of the recent observation that the black hole entropy is the square of the topological string wave-function. This wave-function can be interpreted in the context of flux compactification of all spatial dimensions as providing a physical probability distribution on the moduli space of string compactification. Euclidean time is realized holographically in this setup.https://resolver.caltech.edu/CaltechAUTHORS:20190927-133504041Entropy of Small Black Holes
https://resolver.caltech.edu/CaltechAUTHORS:20110614-104609810
Year: 2006
DOI: 10.1143/PTPS.163.355
I will describe the relation between the entropy of extremal black holes and the topological string partition function.https://resolver.caltech.edu/CaltechAUTHORS:20110614-104609810Baby universes in string theory
https://resolver.caltech.edu/CaltechAUTHORS:DIJprd06
Year: 2006
DOI: 10.1103/PhysRevD.73.066002
We argue that the holographic description of four-dimensional Bogomol'nyi-Prasad-Sommerfield black holes naturally includes multicenter solutions. This suggests that the holographic dual to the gauge theory is not a single AdS2×S2 but a coherent ensemble of them. We verify this in a particular class of examples, where the two-dimensional Yang-Mills theory gives a holographic description of the black holes obtained by branes wrapping Calabi-Yau cycles. Using the free fermionic formulation, we show that O(e-N) nonperturbative effects entangle the two Fermi surfaces. In an Euclidean description, the wave function of the multicenter black holes gets mapped to the Hartle-Hawking wave function of baby universes. This provides a concrete realization, within string theory, of effects that can be interpreted as the creation of baby universes. We find that, at least in the case we study, the baby universes do not lead to a loss of quantum coherence, in accord with general arguments.https://resolver.caltech.edu/CaltechAUTHORS:DIJprd06Baby universes and string theory
https://resolver.caltech.edu/CaltechAUTHORS:20110322-100922722
Year: 2006
DOI: 10.1142/S0218271806008978
The description of 4D BPS black holes in terms of branes wrapped on various cycles in
a Calabi-Yau space gives us the opportunity to study various issues in quantum gravity
in a definite way by means of the worldvolume theory of the branes. In the particular
example discussed here, there is a simple worldvolume description in terms of 2D Yang-Mills
theory. The latter is an exactly solvable system of free fermions in one dimension.
The exact answer for the free energy of this system can be written in a way that suggests
an interpretation in terms of contributions from multiple (baby) universes.https://resolver.caltech.edu/CaltechAUTHORS:20110322-100922722Direct mediation of metastable supersymmetry breaking
https://resolver.caltech.edu/CaltechAUTHORS:KITprd07
Year: 2007
DOI: 10.1103/PhysRevD.75.045022
The supersymmetric SU(NC) Yang-Mills theory coupled to NF matter fields in the fundamental representation has metastable vacua with broken supersymmetry when NChttps://resolver.caltech.edu/CaltechAUTHORS:KITprd07Nondecoupling of Maximal Supergravity from the Superstring
https://resolver.caltech.edu/CaltechAUTHORS:GREprl07
Year: 2007
DOI: 10.1103/PhysRevLett.99.041601
We consider the conditions necessary for obtaining perturbative maximal supergravity in d dimensions as a decoupling limit of type II superstring theory compactified on a (10-d) torus. For dimensions d=2 and d=3, it is possible to define a limit in which the only finite-mass states are the 256 massless states of maximal supergravity. However, in dimensions d>=4, there are infinite towers of additional massless and finite-mass states. These correspond to Kaluza-Klein charges, wound strings, Kaluza-Klein monopoles, or branes wrapping around cycles of the toroidal extra dimensions. We conclude that perturbative supergravity cannot be decoupled from string theory in dimensions >=4. In particular, we conjecture that pure [script N]=8 supergravity in four dimensions is in the Swampland.https://resolver.caltech.edu/CaltechAUTHORS:GREprl07Gauge mediation in string theory
https://resolver.caltech.edu/CaltechAUTHORS:20100924-082214141
Year: 2007
DOI: 10.1016/j.physletb.2007.06.056
We show that a large class of phenomenologically viable models for gauge mediation of supersymmetry breaking based on meta-stable vacua can be realized in local Calabi–Yau compactifications of string theory.https://resolver.caltech.edu/CaltechAUTHORS:20100924-082214141Quantum Entanglement of Baby Universes
https://resolver.caltech.edu/CaltechAUTHORS:20100819-114040490
Year: 2007
DOI: 10.1016/j.nuclphysb.2007.04.006
We study quantum entanglements of baby universes which appear in non-perturbative
corrections to the OSV formula for the entropy of extremal black holes in Type IIA string
theory compactified on the local Calabi-Yau manifold defined as a rank 2 vector bundle
over an arbitrary genus G Riemann surface. This generalizes the result for G = 1 in
hep-th/0504221. Non-perturbative terms can be organized into a sum over contributions
from baby universes, and the total wave-function is their coherent superposition in the third
quantized Hilbert space. We find that half of the universes preserve one set of supercharges
while the other half preserve a different set, making the total universe stable but non-BPS.
The parent universe generates baby universes by brane/anti-brane pair creation, and baby
universes are correlated by conservation of non-normalizable D-brane charges under the
process. There are no other source of entanglement of baby universes, and all possible
states are superposed with the equal weight.https://resolver.caltech.edu/CaltechAUTHORS:20100819-114040490Extremal N = (2, 2) 2D Conformal Field Theories and Constraints of Modularity
https://resolver.caltech.edu/CaltechAUTHORS:20160505-104651886
Year: 2008
DOI: 10.4310/CNTP.2008.v2.n4.a3
We explore the constraints on the spectrum of primary fields implied by modularity of the elliptic genus of N = (2, 2) 2D CFT's. We show that such constraints have nontrivial implications for the existence of "extremal" N = (2, 2) conformal field theories. Applications to AdS_3 supergravity and flux compactifications are addressed.https://resolver.caltech.edu/CaltechAUTHORS:20160505-104651886Metastable vacua in perturbed Seiberg-Witten theories
https://resolver.caltech.edu/CaltechAUTHORS:20090518-095435229
Year: 2008
DOI: 10.48550/arXiv.0704.3613
We show that, for a generic choice of a point on the Coulomb branch of any N = 2 supersymmetric gauge theory, it is possible to find a superpotential perturbation which generates a metastable vacuum at the point. For theories with SU(N) gauge group, such a superpotential can be expressed as a sum of single-trace terms for N = 2 and 3. If the metastable point is chosen at the origin of the moduli space, we can show that the superpotential can be a single-trace operator for any N. In both cases, the superpotential is a polynomial of degree 3N of the vector multiplet scalar field.https://resolver.caltech.edu/CaltechAUTHORS:20090518-095435229Superconformal Chern-Simons theories and the squashed seven sphere
https://resolver.caltech.edu/CaltechAUTHORS:OOGjhep08
Year: 2008
DOI: 10.1088/1126-6708/2008/11/082
We show that there are two supersymmetric completions of the three-dimensional Chern-Simons theory of level k with gauge group U(N) × U(N) coupled to four sets of massless scalars and spinors in the bi-fundamental representation, if we require Sp(2) ⊂ SU(4) global symmetry with the matter fields in the fundamental representation of SU(4). One is the Script N = 6 superconformal theory recently studied in hep-th/0806.1218 and another is a new theory with Script N = 1 superconformal symmetry. We conjecture that the Script N = 1 theory is dual to M theory on AdS4 × squashed S^7/Bbb Zk.https://resolver.caltech.edu/CaltechAUTHORS:OOGjhep08New Anomalies in Topological String Theory
https://resolver.caltech.edu/CaltechAUTHORS:20090819-111703735
Year: 2009
DOI: 10.1143/PTPS.177.120
We show that the topological string partition function with D-branes on a compact Calabi-Yau manifold has new anomalies that spoil the recursive structure of the holomorphic anomaly equation and introduce dependence on wrong moduli (such as complex structure moduli in the A-model), unless the disk one-point functions vanish. This provides a microscopic explanation for the recent result of Walcher in arXiv:0712.2775 on counting of BPS states in M-theory using the topological string partition function. The relevance of vanishing disk one-point functions to large N duality for compact Calabi-Yau manifolds is noted.https://resolver.caltech.edu/CaltechAUTHORS:20090819-111703735Current correlators for general gauge mediation
https://resolver.caltech.edu/CaltechAUTHORS:20090817-101240132
Year: 2009
DOI: 10.1016/j.nuclphysb.2008.09.017
In the gauge mediation mechanism, the effects of the hidden sector are characterized by a set of correlation functions of the global symmetry current of the hidden sector. We present methods to compute these correlators in cases with strongly coupled hidden sectors. Several examples are presented to demonstrate the technique explicitly.https://resolver.caltech.edu/CaltechAUTHORS:20090817-101240132Emergent Calabi-Yau geometry
https://resolver.caltech.edu/CaltechAUTHORS:20090804-095624246
Year: 2009
DOI: 10.1103/PhysRevLett.102.161601
We show how the smooth geometry of Calabi-Yau manifolds emerges from the thermodynamic limit of the statistical mechanical model of crystal melting defined in our previous paper. In particular, the thermodynamic partition function of molten crystals is shown to be equal to the classical limit of the partition function of the topological string theory by relating the Ronkin function of the characteristic polynomial of the crystal melting model to the holomorphic 3-form on the corresponding Calabi-Yau manifold.https://resolver.caltech.edu/CaltechAUTHORS:20090804-095624246Crystal Melting and Toric Calabi-Yau Manifolds
https://resolver.caltech.edu/CaltechAUTHORS:20090911-153603164
Year: 2009
DOI: 10.1007/s00220-009-0836-y
We construct a statistical model of crystal melting to count BPS bound states of D0 and D2 branes on a single D6 brane wrapping an arbitrary toric Calabi-Yau threefold. The three-dimensional crystalline structure is determined by the quiver diagram and the brane tiling which characterize the low energy effective theory of D branes. The crystal is composed of atoms of different colors, each of which corresponds to a node of the quiver diagram, and the chemical bond is dictated by the arrows of the quiver diagram. BPS states are constructed by removing atoms from the crystal. This generalizes the earlier results on the BPS state counting to an arbitrary non-compact toric Calabi-Yau manifold. We point out that a proper understanding of the relation between the topological string theory and the crystal melting involves the wall crossing in the Donaldson-Thomas theory.https://resolver.caltech.edu/CaltechAUTHORS:20090911-153603164Geometry as seen by string theory
https://resolver.caltech.edu/CaltechAUTHORS:20100121-141325818
Year: 2009
DOI: 10.1007/s11537-009-0833-0
This is an introductory review of the topological string theory from physicist's perspective. I start with the definition of the theory and describe its relation to the Gromov–Witten invariants. The BCOV holomorphic anomaly equations, which generalize the Quillen anomaly formula, can be used to compute higher genus partition functions of the theory. The open/closed string duality relates the closed topological string theory to the Chern–Simons gauge theory and the random matrix model. As an application of the topological string theory, I discuss the counting of bound states of D-branes.https://resolver.caltech.edu/CaltechAUTHORS:20100121-141325818Supersymmetric non-relativistic geometries in M-theory
https://resolver.caltech.edu/CaltechAUTHORS:20091203-101126154
Year: 2010
DOI: 10.1016/j.nuclphysb.2009.08.021
We construct M-theory supergravity solutions with the non-relativistic Schrödinger symmetry starting
from the warped AdS_5 metric with N = 1 supersymmetry. We impose the condition that the lightlike direction
is compact by making it a non-trivial U(1) bundle over the compact space. Sufficient conditions
for such solutions are analyzed. The solutions have two supercharges for generic values of parameters,
but the number of supercharges increases to six in some special cases. A Schrödinger geometry with
SU(2)×SU(2)×U(1) isometry is considered as a specific example.We consider the Kaluza–Klein modes
and show that the non-relativistic particle number is bounded above by the quantum numbers of the compact
space.https://resolver.caltech.edu/CaltechAUTHORS:20091203-101126154Gravity dual of spatially modulated phase
https://resolver.caltech.edu/CaltechAUTHORS:20100413-155824837
Year: 2010
DOI: 10.1103/PhysRevD.81.044018
We show that the five-dimensional Maxwell theory with the Chern-Simons term is tachyonic in the presence of a constant electric field. When coupled to gravity, a sufficiently large Chern-Simons coupling causes instability of the Reissner-Nordström black holes in anti-de Sitter space. The instability happens only at nonvanishing momenta, suggesting a spatially modulated phase in the holographically dual quantum field theory in (3+1) dimensions, with spontaneous current generation in a helical configuration. The three-charge extremal black hole in the type IIB superstring theory on AdS_5×S^5 barely satisfies the stability condition.https://resolver.caltech.edu/CaltechAUTHORS:20100413-155824837Supersymmetry Breaking and Gauge Mediation
https://resolver.caltech.edu/CaltechAUTHORS:20110329-080256247
Year: 2010
DOI: 10.1146/annurev.nucl.012809.104540
We review recent works on supersymmetry breaking and gauge mediation. We survey our current understanding of dynamical supersymmetry-breaking mechanisms and describe new model-building tools that use duality, metastability, and stringy construction. We discuss phenomenological constraints and their solutions, paying particular attention to gaugino masses and electroweak symmetry breaking.https://resolver.caltech.edu/CaltechAUTHORS:20110329-080256247Holographic endpoint of spatially modulated phase transition
https://resolver.caltech.edu/CaltechAUTHORS:20110420-110435590
Year: 2010
DOI: 10.1103/PhysRevD.82.126001
In a previous paper [S. Nakamura, H. Ooguri, and C. S. Park, Phys. Rev. D 81, 044018 (2010)], we showed that the Reissner-Nordström black hole in the five-dimensional anti–de Sitter space coupled to the Maxwell theory with the Chern-Simons term is unstable when the Chern-Simons coupling is sufficiently large. In the dual conformal field theory, the instability suggests a spatially modulated phase transition. In this paper, we construct and analyze nonlinear solutions which describe the endpoint of this phase transition. In the limit where the Chern-Simons coupling is large, we find that the phase transition is of the second order with the mean field critical exponent. However, the dispersion relation with the Van Hove singularity enhances quantum corrections in the bulk, and we argue that this changes the order of the phase transition from the second to the first. We compute linear response functions in the nonlinear solution and find an infinite off-diagonal DC conductivity in the new phase.https://resolver.caltech.edu/CaltechAUTHORS:20110420-110435590Spatially Modulated Phase in the Holographic Description of Quark-Gluon Plasma
https://resolver.caltech.edu/CaltechAUTHORS:20110317-104913163
Year: 2011
DOI: 10.1103/PhysRevLett.106.061601
We present a string theory construction of a gravity dual of a spatially modulated phase. Our earlier work shows that the Chern-Simons
term in the five-dimensional Maxwell theory destabilizes the
Reissner-Nordstrom black holes in anti-de Sitter space if the
Chern-Simons coupling is sufficiently high. In this Letter, we show
that a similar instability is realized on the world volume of 8-branes
in the Sakai-Sugimoto model in the quark-gluon plasma phase. Our result
suggests a new spatially modulated phase in quark-gluon plasma when the
baryon density is above 0.8N_f fm(^-3) at temperature 150 MeV.https://resolver.caltech.edu/CaltechAUTHORS:20110317-104913163Wall Crossing and M-Theory
https://resolver.caltech.edu/CaltechAUTHORS:20111216-141905707
Year: 2011
DOI: 10.2977/PRIMS/44
We study BPS bound states of D0 and D2 branes on a single D6 brane wrapping a Calabi-Yau 3-fold X. When X has no compact 4-cycles, the BPS bound states are organized into a free field Fock space, whose generators correspond to BPS states of spinning M2 branes in M-theory compactified down to 5 dimensions by a Calabi-Yau 3-fold X. The generating function of the D-brane bound states is expressed as a reduction of the square of the topological string partition function, in all chambers of the Kähler moduli space.https://resolver.caltech.edu/CaltechAUTHORS:20111216-141905707Wall Crossing as Seen by Matrix Models
https://resolver.caltech.edu/CaltechAUTHORS:20111221-133839011
Year: 2011
DOI: 10.1007/s00220-011-1330-x
The number of BPS bound states of D-branes on a Calabi-Yau manifold depends on two sets of data, the BPS charges and the stability conditions. For D0 and D2-branes bound to a single D6-brane wrapping a Calabi-Yau 3-fold X, both are naturally related to the Kähler moduli space M(X). We construct unitary one-matrix models which count such BPS states for a class of toric Calabi-Yau manifolds at infinite 't Hooft coupling. The matrix model for the BPS counting on X turns out to give the topological string partition function for another Calabi-Yau manifold Y, whose Kähler moduli space M(Y) contains two copies of M(X), one related to the BPS charges and another to the stability conditions. The two sets of data are unified in M(Y). The matrix models have a number of other interesting features. They compute spectral curves and mirror maps relevant to the remodeling conjecture. For finite 't Hooft coupling they give rise to yet more general geometry Y containing Y.https://resolver.caltech.edu/CaltechAUTHORS:20111221-133839011Notes on the K3 Surface and the Mathieu Group M_(24)
https://resolver.caltech.edu/CaltechAUTHORS:20111014-150332394
Year: 2011
DOI: 10.1080/10586458.2011.544585
We point out that the elliptic genus of the K3 surface has a natural decomposition in terms of dimensions of irreducible representations of the largest Mathieu group M_(24). The reason remains a mystery.https://resolver.caltech.edu/CaltechAUTHORS:20111014-150332394Comments on worldsheet description of the Omega background
https://resolver.caltech.edu/CaltechAUTHORS:20120224-134308688
Year: 2012
DOI: 10.1016/j.nuclphysb.2011.11.010
Nekrasovʼs partition function is defined on a flat bundle of R^4 over S^1 called the Omega background. When the fibration is self-dual, the partition function is known to be equal to the topological string partition function, which computes scattering amplitudes of self-dual gravitons and graviphotons in type II superstring compactified on a Calabi–Yau manifold. We propose a generalization of this correspondence when the fibration is not necessarily self-dual.https://resolver.caltech.edu/CaltechAUTHORS:20120224-134308688Instability in Magnetic Materials with a Dynamical Axion Field
https://resolver.caltech.edu/CaltechAUTHORS:20120103-143444619
Year: 2012
DOI: 10.1103/PhysRevLett.108.161803
It has been pointed out that axion electrodynamics exhibits instability in the presence of a background electric field. We show that the instability leads to a complete screening of an applied electric field above a certain critical value and the excess energy is converted into a magnetic field. We clarify the physical origin of the screening effect and discuss its possible experimental realization in magnetic materials where magnetic fluctuations play the role of the dynamical axion field.https://resolver.caltech.edu/CaltechAUTHORS:20120103-143444619Spontaneous Generation of Angular Momentum in Holographic Theories
https://resolver.caltech.edu/CaltechAUTHORS:20130708-104924811
Year: 2013
DOI: 10.1103/PhysRevLett.110.211601
The Schwarzschild black two-brane in four-dimensional anti–de Sitter space is dual to a finite temperature state in three-dimensional conformal field theory. We show that the solution acquires a nonzero angular momentum density when a gravitational Chern-Simons coupling is turned on in the bulk, even though the solution is not modified. A similar phenomenon is found for the Reissner-Nordström black two-brane with axionic coupling to the gauge field. We discuss interpretation of this phenomenon from the point of view of the boundary three-dimensional conformal field theory.https://resolver.caltech.edu/CaltechAUTHORS:20130708-104924811Modular Constraints on Calabi-Yau Compactifications
https://resolver.caltech.edu/CaltechAUTHORS:20131111-095649297
Year: 2013
DOI: 10.1007/s00220-013-1797-8
We derive global constraints on the non-BPS sector of supersymmetric 2d sigma-models whose target space is a Calabi-Yau manifold. When the total Hodge number of the Calabi-Yau threefold is sufficiently large, we show that there must be non-BPS primary states whose total conformal weights are less than 0.656. Moreover, the number of such primary states grows at least linearly in the total Hodge number. We discuss implications of these results for Calabi-Yau geometry.https://resolver.caltech.edu/CaltechAUTHORS:20131111-095649297Out of equilibrium temperature from holography
https://resolver.caltech.edu/CaltechAUTHORS:20140122-121855825
Year: 2013
DOI: 10.1103/PhysRevD.88.126003
We define an effective temperature and study its properties for a class of out-of-equilibrium steady states in a heat bath. Our analysis is based on the anti-de Sitter spacetime/conformal field theory (AdS/CFT) correspondence, and examples include systems driven by applied electric fields and branes dragged in plasmas. We found that the effective temperature can be lower than that of the heat bath and that the out-of-equilibrium noise can be smaller than that in equilibrium. We show that a generalization of the fluctuation-dissipation relation holds for the effective temperature. In particular, we generalize the Johnson-Nyquist relation for a large electric field.https://resolver.caltech.edu/CaltechAUTHORS:20140122-121855825Angular momentum generation by parity violation
https://resolver.caltech.edu/CaltechAUTHORS:20140814-092632811
Year: 2014
DOI: 10.1103/PhysRevD.89.106007
We generalize our holographic derivation of spontaneous angular momentum generation in 2+1 dimensions in several directions. We consider cases when a parity-violating perturbation responsible for the angular momentum generation can be nonmarginal (while in our previous paper we restricted to a marginal perturbation), including all possible two-derivative interactions, with parity violations triggered both by gauge and gravitational Chern-Simons terms in the bulk. We make only a minimal assumption about the bulk geometry that it is asymptotically AdS, respects the Poincaré symmetry in 2+1 dimensions, and has a horizon. In this generic setup, we find a remarkably concise and universal formula for the expectation value of the angular momentum density, to all orders in the parity violating perturbation.https://resolver.caltech.edu/CaltechAUTHORS:20140814-092632811Hall Viscosity and Angular Momentum in Gapless Holographic Models
https://resolver.caltech.edu/CaltechAUTHORS:20161219-092554100
Year: 2014
DOI: 10.1103/PhysRevD.90.086007
We use the holographic approach to compare the Hall viscosity η_H and the angular momentum density J in gapless systems in 2+1 dimensions at finite temperature. We start with a conformal fixed point and turn on a perturbation which breaks the parity and time-reversal symmetries via gauge and gravitational Chern-Simons couplings in the bulk. While the ratio of η_H and J shows some universal properties when the perturbation is slightly relevant, we find that the two quantities behave differently in general. In particular, η_H depends only on infrared physics, while J receives contributions from degrees of freedom at all scales.https://resolver.caltech.edu/CaltechAUTHORS:20161219-092554100Locality of Gravitational Systems from Entanglement of Conformal Field Theories
https://resolver.caltech.edu/CaltechAUTHORS:20150616-152928658
Year: 2015
DOI: 10.1103/PhysRevLett.114.221601
The Ryu-Takayanagi formula relates the entanglement entropy in a conformal field theory to the area of
a minimal surface in its holographic dual. We show that this relation can be inverted for any state in the
conformal field theory to compute the bulk stress-energy tensor near the boundary of the bulk spacetime,
reconstructing the local data in the bulk from the entanglement on the boundary. We also show that
positivity, monotonicity, and convexity of the relative entropy for small spherical domains between the
reduced density matrices of any state and of the ground state of the conformal field theory are guaranteed by
positivity conditions on the bulk matter energy density. As positivity and monotonicity of the relative
entropy are general properties of quantum systems, this can be interpreted as a derivation of bulk energy
conditions in any holographic system for which the Ryu-Takayanagi prescription applies. We discuss an
information theoretical interpretation of the convexity in terms of the Fisher metric.https://resolver.caltech.edu/CaltechAUTHORS:20150616-152928658The Holographic Entropy Cone
https://resolver.caltech.edu/CaltechAUTHORS:20150616-154806338
Year: 2015
DOI: 10.1007/JHEP09(2015)130
We initiate a systematic enumeration and classification of entropy inequalities satisfied by the Ryu-Takayanagi formula for conformal field theory states with smooth holographic dual geometries. For 2, 3, and 4 regions, we prove that the strong subadditivity and the monogamy of mutual information give the complete set of inequalities. This is in contrast to the situation for generic quantum systems, where a complete set of entropy inequalities is not known for 4 or more regions. We also find an infinite new family of inequalities applicable to 5 or more regions. The set of all holographic entropy inequalities bounds the phase space of Ryu-Takayanagi entropies, defining the holographic entropy cone. We characterize this entropy cone by reducing geometries to minimal graph models that encode the possible cutting and gluing relations of minimal surfaces. We find that, for a fixed number of regions, there are only finitely many independent entropy inequalities. To establish new holographic entropy inequalities, we introduce a combinatorial proof technique that may also be of independent interest in Riemannian geometry and graph theory.https://resolver.caltech.edu/CaltechAUTHORS:20150616-154806338Bulk Locality and Boundary Creating Operators
https://resolver.caltech.edu/CaltechAUTHORS:20150812-140634734
Year: 2015
DOI: 10.1007/JHEP10(2015)114
We formulate a minimum requirement for CFT operators to be localized in the dual AdS. In any spacetime dimensions, we show that a general solution to the requirement is a linear superposition of operators creating spherical boundaries in CFT, with the dilatation by the imaginary unit from their centers. This generalizes the recent proposal by Miyaji et al. for bulk local operators in the three dimensional AdS. We show that Ishibashi states for the global conformal symmetry in any dimensions and with the imaginary di-latation obey free field equations in AdS and that incorporating bulk interactions require their superpositions. We also comment on the recent proposals by Kabat et al., and by H. Verlinde.https://resolver.caltech.edu/CaltechAUTHORS:20150812-140634734Reflections on Conformal Spectra
https://resolver.caltech.edu/CaltechAUTHORS:20151104-124350087
Year: 2016
DOI: 10.1007/JHEP04(2016)184
We use modular invariance and crossing symmetry of conformal field theory to reveal approximate reflection symmetries in the spectral decompositions of the partition function in two dimensions in the limit of large central charge and of the four-point function in any dimension in the limit of large scaling dimensions Δ0 of external operators. We use these symmetries to motivate universal upper bounds on the spectrum and the operator product expansion coefficients, which we then derive by independent techniques. Some of the bounds for four-point functions are valid for finite Δ0 as well as for large Δ0. We discuss a similar symmetry in a large spacetime dimension limit. Finally, we comment on the analogue of the Cardy formula and sparse light spectrum condition for the four-point function.https://resolver.caltech.edu/CaltechAUTHORS:20151104-124350087Bulk Local States and Crosscaps in Holographic CFT
https://resolver.caltech.edu/CaltechAUTHORS:20160509-164600548
Year: 2016
DOI: 10.1007/JHEP10(2016)085
In a weakly coupled gravity theory in the anti-de Sitter space, local states in the bulk are linear superpositions of Ishibashi states for a crosscap in the dual conformal field theory. The superposition structure can be constrained either by the microscopic causality in the bulk gravity or the bootstrap condition in the boundary conformal field theory. We show, contrary to some expectation, that these two conditions are not compatible to each other in the weak gravity regime. We also present an evidence to show that bulk local states in three dimensions are not organized by the Virasoro symmetry.https://resolver.caltech.edu/CaltechAUTHORS:20160509-164600548Gravitational Positive Energy Theorems from Information Inequalities
https://resolver.caltech.edu/CaltechAUTHORS:20161220-092051390
Year: 2016
DOI: 10.1093/ptep/ptw139
In this paper we argue that classical asymptotically anti-de Sitter spacetimes that arise as states in consistent ultraviolet completions of Einstein gravity coupled to matter must satisfy an infinite family of positive energy conditions. To each ball-shaped spatial region B of the boundary spacetime we can associate a bulk spatial region Σ_B between B and the bulk extremal surface
B
with the same boundary as B. We show that there exists a natural notion of a gravitational energy for every such region that is non-negative, and non-increasing as one makes the region smaller. The results follow from identifying this gravitational energy with a quantum relative entropy in the associated dual conformal field theory state. The positivity and monotonicity properties of the gravitational energy are implied by the positivity and monotonicity of relative entropy, which holds universally in all quantum systems.https://resolver.caltech.edu/CaltechAUTHORS:20161220-092051390Shortening Anomalies in Supersymmetric Theories
https://resolver.caltech.edu/CaltechAUTHORS:20161114-154042042
Year: 2017
DOI: 10.1007/JHEP01(2017)067
We present new anomalies in two-dimensiona N=(2,2) superconformal theories. They obstruct the shortening conditions of chiral and twisted chiral multiplets at coincident points. This implies that marginal couplings cannot be promoted to background superfields in short representations. Therefore, standard results that follow from N=(2,2) spurion analysis are invalidated. These anomalies appear only if supersymmetry is enhanced beyond N=(2,2). These anomalies explain why the conformal manifolds of the K3 and T^4 sigma models are not Kähler and do not factorize into chiral and twisted chiral moduli spaces and why there are no N=(2,2) gauged linear sigma models that cover these conformal manifolds. We also present these results from the point of view of the Riemann curvature of conformal manifolds.https://resolver.caltech.edu/CaltechAUTHORS:20161114-154042042Non-supersymmetric AdS and the Swampland
https://resolver.caltech.edu/CaltechAUTHORS:20161024-200308753
Year: 2017
DOI: 10.4310/ATMP.2017.v21.n7.a8
We propose to sharpen the weak gravity conjecture by the statement that, except for BPS states in a supersymmetric theory, the gravitational force is strictly weaker than any electric force and provide a number of evidences for this statement. Our conjecture implies that any non-supersymmetric anti-de Sitter vacuum supported by fluxes must be unstable, as is the case for all known attempts at such holographic constructions.https://resolver.caltech.edu/CaltechAUTHORS:20161024-200308753New Kaluza-Klein Instantons and Decay of AdS Vacua
https://resolver.caltech.edu/CaltechAUTHORS:20170314-133249092
Year: 2017
DOI: 10.1103/PhysRevD.96.026016
We construct a generalization of Witten's Kaluza-Klein instanton, where a higher-dimensional sphere (rather than a circle as in Witten's instanton) collapses to zero size and the geometry terminates at a bubble of nothing, in a low energy effective theory of M theory. We use the solution to exhibit the instability of nonsupersymmetric AdS_5 vacua in M theory compactified on positive Kähler-Einstein spaces, providing further evidence for the recent conjecture that any nonsupersymmetric anti–de Sitter vacuum supported by fluxes must be unstable.https://resolver.caltech.edu/CaltechAUTHORS:20170314-133249092Distinguishability of black hole microstates
https://resolver.caltech.edu/CaltechAUTHORS:20170918-091256373
Year: 2017
DOI: 10.1103/PhysRevD.96.066017
We use the Holevo information to estimate distinguishability of microstates of a black hole in anti-de Sitter space by measurements one can perform on a subregion of a Cauchy surface of the dual conformal field theory. We find that microstates are not distinguishable at all until the subregion reaches a certain size and that perfect distinguishability can be achieved before the subregion covers the entire Cauchy surface. We will compare our results with expectations from the entanglement wedge reconstruction, tensor network models, and the bit threads interpretation of the Ryu-Takayanagi formula.https://resolver.caltech.edu/CaltechAUTHORS:20170918-091256373Distance and de Sitter Conjectures on the Swampland
https://resolver.caltech.edu/CaltechAUTHORS:20181115-093945553
Year: 2019
DOI: 10.1016/j.physletb.2018.11.018
Among Swampland conditions, the distance conjecture characterizes the geometry of scalar fields and the de Sitter conjecture constrains allowed potentials on it. We point out a connection between the distance conjecture and a refined version of the de Sitter conjecture in any parametrically controlled regime of string theory by using Bousso's covariant entropy bound. The refined version turns out to evade all counter-examples at scalar potential maxima that have been raised. We comment on the relation of our result to the Dine–Seiberg problem.https://resolver.caltech.edu/CaltechAUTHORS:20181115-093945553Constraints on Symmetries from Holography
https://resolver.caltech.edu/CaltechAUTHORS:20190517-095643873
Year: 2019
DOI: 10.1103/PhysRevLett.122.191601
In this Letter we show that a set of old conjectures about symmetries in quantum gravity hold within the anti–de Sitter/conformal field theory correspondence. These conjectures are that no global symmetries are possible, that internal gauge symmetries must come with dynamical objects that transform in all irreducible representations, and that internal gauge groups must be compact. These conjectures are not obviously true from a bulk perspective, they are nontrivial consequences of the nonperturbative consistency of the correspondence. More details of and background for these arguments are presented in an accompanying paper.https://resolver.caltech.edu/CaltechAUTHORS:20190517-095643873Light-cone modular bootstrap and pure gravity
https://resolver.caltech.edu/CaltechAUTHORS:20190709-155709037
Year: 2019
DOI: 10.1103/PhysRevD.100.066029
We explore the large spin spectrum in two-dimensional conformal field theories with a finite twist gap, using the modular bootstrap in the light-cone limit. By recursively solving the modular crossing equations associated with different PSL(2,Z) elements, we identify the universal contribution to the density of large spin states from the vacuum in the dual channel. Our result takes the form of a sum over PSL(2,Z) elements, whose leading term generalizes the usual Cardy formula to a wider regime. Rather curiously, the contribution to the density of states from the vacuum becomes negative in a specific limit, which can be canceled by that from a nonvacuum Virasoro primary whose twist is no bigger than c−1/16. This suggests a new upper bound of c−1/16 on the twist gap in any c>1 compact, unitary conformal field theory with a vacuum, which would in particular imply that pure AdS_3 gravity does not exist. We confirm this negative density of states in the pure gravity partition function by Maloney, Witten, and Keller. We generalize our discussion to theories with N=(1,1) supersymmetry and find similar results.https://resolver.caltech.edu/CaltechAUTHORS:20190709-155709037The High Energy Behavior of Mellin Amplitudes
https://resolver.caltech.edu/CaltechAUTHORS:20200205-143527298
Year: 2020
DOI: 10.1103/PhysRevD.101.066008
In any consistent massive quantum field theory there are well-known bounds on scattering amplitudes at high energies. In conformal field theory there is no scattering amplitude, but the Mellin amplitude is a well-defined object analogous to the scattering amplitude. We prove bounds at high energies on Mellin amplitudes in conformal field theories, valid under certain technical assumptions. Such bounds are derived by demanding the absence of spurious singularities in position space correlators. We also conjecture a stronger bound, based on evidence from several explicit examples.https://resolver.caltech.edu/CaltechAUTHORS:20200205-143527298Twist Gap and Global Symmetry in Two Dimensions
https://resolver.caltech.edu/CaltechAUTHORS:20200408-133007156
Year: 2020
DOI: 10.1103/PhysRevD.101.106026
We show that every compact, unitary two-dimensional conformal field theory with an Abelian conserved current has vanishing twist gap for charged primary fields with respect to the u(1)×Virasoro algebra. This means that either the chiral algebra is enhanced by a charged primary field with zero twist or there is an infinite family of charged primary fields that accumulate to zero twist.https://resolver.caltech.edu/CaltechAUTHORS:20200408-133007156Duality and axionic weak gravity
https://resolver.caltech.edu/CaltechAUTHORS:20200504-141139669
Year: 2020
DOI: 10.1103/PhysRevD.102.046008
The axionic weak gravity conjecture predicts the existence of instantons whose actions are less than their charges in appropriate units. We show that the conjecture is satisfied for the axion-dilaton-gravity system if we assume duality constraints on the higher derivative corrections in addition to positivity bounds which follow from unitarity, analyticity, and locality of UV scattering amplitudes. On the other hand, the conjecture does not follow if we assume the positivity bounds only. This presents an example where derivation of the weak gravity conjecture requires more detailed UV information than the consistency of scattering amplitudes.https://resolver.caltech.edu/CaltechAUTHORS:20200504-141139669Singularities of thermal correlators at strong coupling
https://resolver.caltech.edu/CaltechAUTHORS:20210421-153703789
Year: 2021
DOI: 10.1103/physrevd.103.066018
We analyze the singularities of the two-point function in a conformal field theory at finite temperature. In a free theory, the only singularity is along the boundary light cone. In the holographic limit, a new class of singularities emerges since two boundary points can be connected by a nontrivial null geodesic in the bulk, encircling the photon sphere of the black hole. We show that these new singularities are resolved by tidal effects due to the black hole curvature, by solving the string world sheet theory in the Penrose limit. Singularities in the asymptotically flat black hole geometry are also discussed.https://resolver.caltech.edu/CaltechAUTHORS:20210421-153703789On rational points in CFT moduli spaces
https://resolver.caltech.edu/CaltechAUTHORS:20201118-103403846
Year: 2021
DOI: 10.1007/JHEP04(2021)067
Motivated by the search for rational points in moduli spaces of two-dimensional conformal field theories, we investigate how points with enhanced symmetry algebras are distributed there. We first study the bosonic sigma-model with S1 target space in detail and uncover hitherto unknown features. We find for instance that the vanishing of the twist gap, though true for the S1 example, does not automatically follow from enhanced symmetry points being dense in the moduli space. We then explore the supersymmetric sigma-model on K3 by perturbing away from the torus orbifold locus. Though we do not reach a definite conclusion on the distribution of enhanced symmetry points in the K3 moduli space, we make several observations on how chiral currents can emerge and disappear under conformal perturbation theory.https://resolver.caltech.edu/CaltechAUTHORS:20201118-103403846Symmetries in Quantum Field Theory and Quantum Gravity
https://resolver.caltech.edu/CaltechAUTHORS:20210406-085746056
Year: 2021
DOI: 10.1007/s00220-021-04040-y
In this paper we use the AdS/CFT correspondence to refine and then establish a set of old conjectures about symmetries in quantum gravity. We first show that any global symmetry, discrete or continuous, in a bulk quantum gravity theory with a CFT dual would lead to an inconsistency in that CFT, and thus that there are no bulk global symmetries in AdS/CFT. We then argue that any "long-range" bulk gauge symmetry leads to a global symmetry in the boundary CFT, whose consistency requires the existence of bulk dynamical objects which transform in all finite-dimensional irreducible representations of the bulk gauge group. We mostly assume that all internal symmetry groups are compact, but we also give a general condition on CFTs, which we expect to be true quite broadly, which implies this. We extend all of these results to the case of higher-form symmetries. Finally we extend a recently proposed new motivation for the weak gravity conjecture to more general gauge groups, reproducing the "convex hull condition" of Cheung and Remmen. An essential point, which we dwell on at length, is precisely defining what we mean by gauge and global symmetries in the bulk and boundary. Quantum field theory results we meet while assembling the necessary tools include continuous global symmetries without Noether currents, new perspectives on spontaneous symmetry-breaking and 't Hooft anomalies, a new order parameter for confinement which works in the presence of fundamental quarks, a Hamiltonian lattice formulation of gauge theories with arbitrary discrete gauge groups, an extension of the Coleman–Mandula theorem to discrete symmetries, and an improved explanation of the decay π⁰→γγ in the standard model of particle physics. We also describe new black hole solutions of the Einstein equation in d+1 dimensions with horizon topology T^p×S^(d−p−1).https://resolver.caltech.edu/CaltechAUTHORS:20210406-085746056Narain to Narnia
https://resolver.caltech.edu/CaltechAUTHORS:20210408-122435918
Year: 2022
DOI: 10.1007/s00220-021-04211-x
We generalize the holographic correspondence between topological gravity coupled to an abelian Chern–Simons theory in three dimensions and an ensemble average of Narain's family of massless free bosons in two dimensions, discovered by Afkhami-Jeddi et al. and by Maloney and Witten. We find that the correspondence also works for toroidal orbifolds but not for K3 or Calabi–Yau sigma-models and not always for the minimal models. We conjecture that the correspondence requires that the central charge is equal to the critical central charge defined by the asymptotic density of states of the chiral algebra. For toroidal orbifolds, we extend the holographic correspondence to correlation functions of twist operators by using topological properties of rational tangles in the three-dimensional ball, which represent configurations of vortices associated to a discrete gauge symmetry.https://resolver.caltech.edu/CaltechAUTHORS:20210408-122435918A universal formula for the density of states in theories with finite-group symmetry
https://resolver.caltech.edu/CaltechAUTHORS:20210922-181613283
Year: 2022
DOI: 10.1088/1361-6382/ac5db2
In this paper we use Euclidean gravity to derive a simple formula for the density of black hole microstates which transform in each irreducible representation of any finite gauge group. Since each representation appears with nonzero density, this gives a new proof of the completeness hypothesis for finite gauge fields. Inspired by the generality of the argument we further propose that the formula applies at high energy in any quantum field theory with a finite-group global symmetry, and give some evidence for this conjecture.https://resolver.caltech.edu/CaltechAUTHORS:20210922-181613283Universal formula for the density of states with continuous symmetry
https://authors.library.caltech.edu/records/skrax-s4s40
Year: 2023
DOI: 10.1103/physrevd.107.026021
<p>We consider a 𝑑-dimensional unitary conformal field theory with a compact Lie group global symmetry 𝐺 and show that, at high temperature 𝑇 and on a compact Cauchy surface, the probability of a randomly chosen state being in an irreducible unitary representation 𝑅 of 𝐺 is proportional to (dim 𝑅)2²exp[−𝑐₂(𝑅)/(𝑏𝑇^(𝑑−1))]. We use the spurion analysis to derive this formula and relate the constant 𝑏 to a domain wall tension. We also verify it for free field theories and holographic conformal field theories and compute 𝑏 in these cases. This generalizes the result in <span class="monospace">2109.03838</span> that the probability is proportional to (dim𝑅)² when 𝐺 is a finite group. As a byproduct of this analysis, we clarify thermodynamical properties of black holes with non-Abelian hair in anti–de Sitter space.</p>
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