arXiv subjects

Gautam Mandal

Publications and source records attributed to Gautam Mandal.

At least 37 records · Page 2Linked to original sources

arXiv2014

The inside outs of AdS(3)/CFT(2): Exact AdS wormholes with entangled CFT duals

We present the complete family of solutions of 3D gravity (Lambda<0) with two asymptotically AdS exterior regions. The solutions are constructed from data at the two boundaries, which correspond to two independent and arbitrary stress tensors T_R, \bar T_R, and T_L, \bar T_L. The two exteriors are smoothly joined on to an interior region through a regular horizon. We find CFT duals of these geometries which are entangled states of two CFT's. We compute correlators between general operators at the two boundaries and find perfect agreement between CFT and bulk calculations. We calculate and match the CFT entanglement entropy (EE) with the holographic EE which involves geodesics passing through the wormhole. We also compute a holographic, non-equilibrium entropy for the CFT using properties of the regular horizon. The construction of the bulk solutions here uses an exact version of Brown-Henneaux type diffeomorphisms which are asymptotically nontrivial and transform the CFT states by two independent unitary operators on the two sides. Our solutions provide an infinite family of explicit examples of the ER=EPR relation of Maldacena and Susskind [arXiv:1306.0533].

hep-th↗

arXiv2013

Dynamical entanglement entropy with angular momentum and U(1) charge

We consider time-dependent entanglement entropy (EE) for a 1+1 dimensional CFT in the presence of angular momentum and U(1) charge. The EE saturates, irrespective of the initial state, to the grand canonical entropy after a time large compared with the length of the entangling interval. We reproduce the CFT results from an AdS dual consisting of a spinning BTZ black hole and a flat U(1) connection. The apparent discrepancy that the holographic EE does not a priori depend on the U(1) charge while the CFT EE does, is resolved by the charge-dependent shift between the bulk and boundary stress tensors. We show that for small entangling intervals, the entanglement entropy obeys the first law of thermodynamics, as conjectured recently. The saturation of the EE in the field theory is shown to follow from a version of quantum ergodicity; the derivation indicates that it should hold for conformal as well as massive theories in any number of dimensions.

hep-th↗

arXiv2013

Double Trace Flows and Holographic RG in dS/CFT correspondence

If there is a dS/CFT correspondence, time evolution in the bulk should translate to RG flows in the dual euclidean field theory. Consequently, although the dual field is expected to be non-unitary, its RG flows will carry an imprint of the unitary time evolution in the bulk. In this note we examine the prediction of holographic RG in de Sitter space for the flow of double and triple trace couplings in any proposed dual. We show quite generally that the correct form of the field theory beta functions for the double trace couplings is obtained from holography, provided one identifies the scale of the field theory with (i|T|) where T is the `time' in conformal coordinates. For dS(4), we find that with an appropriate choice of operator normalization, it is possible to have real n-point correlation functions as well as beta functions with real coefficients. This choice leads to an RG flow with an IR fixed point at negative coupling unlike in a unitary theory where the IR fixed point is at positive coupling. The proposed correspondence of Sp(N) vector models with de Sitter Vasiliev gravity provides a specific example of such a phenomenon. For dS(d+1) with even d, however, we find that no choice of operator normalization exists which ensures reality of coefficients of the beta-functions as well as absence of n-dependent phases for various n-point functions, as long as one assumes real coupling constants in the bulk Lagrangian.

hep-th↗

arXiv2013

Quantum quench in matrix models: Dynamical phase transitions, Selective equilibration and the Generalized Gibbs Ensemble

Quantum quench dynamics is considered in a one dimensional unitary matrix model with a single trace potential. This model is integrable and has been studied in the context of non-critical string theory. We find dynamical phase transitions, and study the role of the quantum critical point. In course of the time evolutions, we find evidence of selective equilibration for a certain class of observables. The equilibrium is governed by the Generalized Gibbs Ensemble (GGE) and differs from the standard Gibbs ensemble. We compute the production of entropy which is O(N) for large N matrices. An important feature of the equilibration is the appearance of an energy cascade, reminiscent of the Richardson cascade in turbulence, where we find flow of energy from initial long wavelength modes to progressively shorter wavelength excitations. We discuss possible implication of the equilibration and of GGE in string theories and higher spin theories. In another related study, we compute time evolutions in a double trace unitary matrix model, which arises as an effective theory of D2 branes in IIA string theory in the confinement phase. We find similar equilibrations and dynamical transitions in this matrix model. The dynamical transitions are related to Gregory-Laflamme transitions in string theory and are potentially connected with the issue of appearance of naked singularities.

hep-th↗

arXiv2012

What is the gravity dual of the confinement/deconfinement transition in holographic QCD?

We study the gravity dual of four dimensional pure Yang-Mills theory through D4 branes, as proposed by Witten (holographic QCD). In this holographic QCD, it has been widely believed that the confinement phase in the pure Yang-Mills theory corresponds to the AdS D4 soliton in gravity and the deconfinement phase corresponds to the black D4 brane. We inspect this conjecture carefully and show that the correspondence between the black D4 brane and the deconfinement phase is not correct. Instead, by using a slightly different set up, we find an alternative gravity solution called "localized soliton", which would be properly related to the deconfinement phase. In this case, the confinement/deconfinement transition is realized as a Gregory-Laflamme type transition. We find that our proposal naturally explains several known properties of QCD.

hep-th↗

arXiv2012

Gregory-Laflamme as the confinement/deconfinement transition in holographic QCD

We discuss the phase structure of N D4 branes wrapped on a temporal (Euclidean) and a spatial circle, in terms of the near-horizon AdS geometries. This system has been studied previously to understand four dimensional pure SU(N) Yang-Mills theory (YM4) through holography. In the usual treatment of the subject, the phase transition between the AdS soliton and the black D4 brane is interpreted as the strong coupling continuation of the confinement/deconfinement transition in YM4. We show that this interpretation is not valid, since the black D4 brane and the deconfinement phase of YM4 have different realizations of the Z_N centre symmetry and cannot be identified. We propose an alternative gravity dual of the confinement/deconfinement transition in terms of a Gregory-Laflamme transition of the AdS soliton in the IIB frame, where the strong coupling continuation of the deconfinement phase of YM4 is a localized D3 soliton. Our proposal offers a new explanation of several aspects of the thermodynamics of holographic QCD. As an example, we show a new mechanism of chiral symmetry restoration in the Sakai-Sugimoto model. The issues discussed in this paper pertain to gravity duals of non-supersymmetric gauge theories in general.

hep-th↗

arXiv2011

Phases of a two dimensional large N gauge theory on a torus

We consider two-dimensional large N gauge theory with D adjoint scalars on a torus, which is obtained from a D+2 dimensional pure Yang-Mills theory on T^{D+2} with D small radii. The two dimensional model has various phases characterized by the holonomy of the gauge field around non-contractible cycles of the 2-torus. We determine the phase boundaries and derive the order of the phase transitions using a method, developed in an earlier work (arxiv:0910.4526), which is nonperturbative in the 'tHooft coupling and uses a 1/D expansion. We embed our phase diagram in the more extensive phase structure of the D+2 dimensional Yang-Mills theory and match with the picture of a cascade of phase transitions found earlier in lattice calculations (arxiv:0710.0098). We also propose a dual gravity system based on a Scherk-Schwarz compactification of a D2 brane wrapped on a 3-torus and find a phase structure which is similar to the phase diagram found in the gauge theory calculation.

hep-th↗

arXiv2011

Holographic Wilsonian flows and emergent fermions in extremal charged black holes

We study holographic Wilsonian RG in a general class of asymptotically AdS backgrounds with a U(1) gauge field. We consider free charged Dirac fermions in such a background, and integrate them up to an intermediate radial distance, yielding an equivalent low energy dual field theory. The new ingredient, compared to scalars, involves a `generalized' basis of coherent states which labels a particular half of the fermion components as coordinates or momenta, depending on the choice of quantization (standard or alternative). We apply this technology to explicitly compute RG flows of charged fermionic operators and their composites (double trace operators) in field theories dual to (a) pure AdS and (b) extremal charged black hole geometries. The flow diagrams and fixed points are determined explicitly. In the case of the extremal black hole, the RG flows connect two fixed points at the UV AdS boundary to two fixed points at the IR AdS_2 region. The double trace flow is shown, both numerically and analytically, to develop a pole singularity in the AdS_2 region at low frequency and near the Fermi momentum, which can be traced to the appearance of massless fermion modes on the low energy cut-off surface. The low energy field theory action we derive exactly agrees with the semi-holographic action proposed by Faulkner and Polchinski in arXiv:1001.5049 [hep-th]. In terms of field theory, the holographic version of Wilsonian RG leads to a quantum theory with random sources. In the extremal black hole background the random sources become `light' in the AdS_2 region near the Fermi surface and emerge as new dynamical degrees of freedom.

hep-th↗

arXiv2010

Phases of one dimensional large N gauge theory in a 1/D expansion

We consider large N Yang Mills theory with D adjoint scalar fields in d dimensions for d=0 or 1. We show the existence of a non-trivial saddle point of the functional integral at large D which is characterized by a mass gap for the adjoint scalars. We integrate out the adjoint scalars in a 1/D expansion around the saddle point. In case of one dimension which is regarded as a circle, this procedure leads to an effective action for the Wilson line. We find an analogue of the confinement/deconfinement transition which consists of a second order phase transition from a uniform to a non-uniform eigenvalue distribution of the Wilson line, closely followed by a Gross-Witten-Wadia transition where a gap develops in the eigenvalue distribution. The phase transition can be regarded as a continuation of a Gregory-Laflamme transition. Our methods involve large values of the dimensionless 'tHooft coupling. The analysis in this paper is quantitatively supported by earlier numerical work for D=9.

hep-th↗

arXiv2009

Renormalization group flows in a Lifshitz-like four fermi model

We study renormalization group flows in the Lifshitz-like $N$-flavour four fermi model discussed in 0905.2928. In the large-$N$ limit, a nontrivial flow occurs in only one of all possible marginal couplings and one relevant coupling, which provides the scale for Lorentz invariance violations. We discuss in detail the phase diagram and RG flows in the space of couplings, which includes the Lifshitz fixed point, the free field fixed point and a new fixed point characterized by $z=1$ scaling and a violation of Lorentz invariance, which cannot be tuned away by adjusting a parameter. In the broken symmetry phase, the model flows from the $z=3$ Lifshitz-like fixed point in the ultraviolet to this new fixed point in the infrared. However, in a modified version of the present model, which has an effective ultraviolet cut-off much smaller than the Lorentz invariance violating scale, the infrared behaviour is governed by an approximately Lorentz invariant theory, similar to the low energy limit of the usual relativistic Nambu$-$Jona-Lasinio model. Such a modified model could be realized by a supersymmetric version of the present model.

hep-th↗

arXiv2009

Asymptotically free four-fermi theory in 4 dimensions at the z=3 Lifshitz-like fixed point

We show that a Nambu-Jona-Lasinio type four-fermion coupling at the z=3 Lifshitz-like fixed point in 3+1 dimensions is asymptotically free and generates a mass scale dynamically. This result is nonperturbative in the limit of a large number of fermion species. The theory is ultra-violet complete and at low energies exhibits Lorentz invariance as an emergent spacetime symmetry. Many of our results generalize to z=d in odd d spatial dimensions; z=d=1 corresponds to the Gross-Neveu model. The above mechanism of mass generation has potential applications to the fermion mass problem and to dynamical electroweak symmetry breaking. We present a scenario in which a composite Higgs field arises from a condensate of these fermions, which then couples to quarks and leptons of the standard model. Such a scenario could eliminate the need for the Higgs potential and the associated hierarchy problem. We also show that the axial anomaly formula at z=3 coincides with the usual one in the relativistic domain.

hep-th↗

arXiv2008

Microstate Dependence of Scattering from the D1-D5 System

We investigate the question of distinguishing between different microstates of the D1-D5 system (with charges Q_1 and Q_5), by scattering with an incoherent beam, composed of a supergravity probe, with central energy E_0 and width (ΔE). The scattering is studied in the dual CFT description in the orbifold limit for finite R, where R is the radius of the circle on which the D1 branes are wrapped. When R(ΔE) >> 1, the absorption cross-section is found to be independent of the microstate and identical to the leading semiclassical answer computed from the naive geometry. For smaller (ΔE), the answer depends on the particular microstate, which we examine for both typical and atypical microstates. We derive an upper bound for the leading correction to the cross-section when 1/R >> ΔE >> (the average energy gap 1/{R [sqrt(Q_1Q_5)]}. For a typical state the bound is proportional to the area of the stretched horizon, [\sqrt(Q_1 Q_5)], up to [log (Q_1Q_5)] terms. Furthermore, when E_0 << (ΔE), the proportionality constant is a pure number independent of all energy scales. Numerical calculations using Lorentzian profiles show that the actual value of the correction is in fact proportional to [sqrt(Q_1Q_5)] without the logarithmic factor. We offer some speculations about how this result can be consistent with a resolution of the naive geometry by higher derivative corrections to supergravity.

hep-th↗

arXiv2008

Local Fluid Dynamical Entropy from Gravity

Spacetime geometries dual to arbitrary fluid flows in strongly coupled N=4 super Yang Mills theory have recently been constructed perturbatively in the long wavelength limit. We demonstrate that these geometries all have regular event horizons, and determine the location of the horizon order by order in a boundary derivative expansion. Intriguingly, the derivative expansion allows us to determine the location of the event horizon in the bulk as a local function of the fluid dynamical variables. We define a natural map from the boundary to the horizon using ingoing null geodesics. The area-form on spatial sections of the horizon can then be pulled back to the boundary to define a local entropy current for the dual field theory in the hydrodynamic limit. The area theorem of general relativity guarantees the positivity of the divergence of the entropy current thus constructed.

hep-th↗

arXiv2007

Supersymmetric Giant Graviton Solutions in AdS_3

We parameterize all classical probe brane configurations that preserve 4 supersymmetries in (a) the extremal D1-D5 geometry, (b) the extremal D1-D5-P geometry, (c) the smooth D1-D5 solutions proposed by Lunin and Mathur and (d) global $AdS_3 \times S_3 \times T^4/K3$. These configurations consist of D1 branes, D5 branes and bound states of D5 and D1 branes with the property that a particular Killing vector is tangent to the brane worldvolume at each point. We show that the supersymmetric sector of the D5 brane worldvolume theory may be analyzed in an effective 1+1 dimensional framework that places it on the same footing as D1 branes. In global AdS and the corresponding Lunin-Mathur solution, the solutions we describe are `bound' to the center of AdS for generic parameters and cannot escape to infinity. We show that these probes only exist on the submanifold of moduli space where the background $B_{NS}$ field and theta angle vanish. We quantize these probes in the near horizon region of the extremal D1-D5 geometry and obtain the theory of long strings discussed by Seiberg and Witten.

hep-th↗

arXiv2007

Dual giant gravitons in AdS$_m$ $\times$ Y$^n$ (Sasaki-Einstein)

We consider BPS motion of dual giant gravitons on Ad$S_5\times Y^5$ where $Y^5$ represents a five-dimensional Sasaki-Einstein manifold. We find that the phase space for the BPS dual giant gravitons is symplectically isomorphic to the Calabi-Yau cone over $Y^5$, with the Kähler form identified with the symplectic form. The quantization of the dual giants therefore coincides with the Kähler quantization of the cone which leads to an explicit correspondence between holomorphic wavefunctions of dual giants and gauge-invariant operators of the boundary theory. We extend the discussion to dual giants in $AdS_4 \times Y^7$ where $Y^7$ is a seven-dimensional Sasaki-Einstein manifold; for special motions the phase space of the dual giants is symplectically isomorphic to the eight-dimensional Calabi-Yau cone.

hep-th↗

arXiv2006

Counting 1/8-BPS Dual-Giants

We count 1/8-BPS states in type IIB string theory on AdS_5 x S^5 background which carry three independent angular momenta on S^5. These states can be counted by considering configurations of multiple dual-giant gravitons up to N in number which share at least four supersymmetries. We map this counting problem to that of counting the energy eigen states of a system of N bosons in a 3-dimensional harmonic oscillator. We also count 1/8-BPS states with two independent non-zero spins in AdS_5 and one non-zero angular momentum on S^5 by considering configurations of arbitrary number of giant gravitons that share at least four supersymmetries.

hep-th↗

arXiv2006

Bosonization of non-relativistic fermions on a circle: Tomonaga's problem revisited

We use the recently developed tools for an exact bosonization of a finite number $N$ of non-relativistic fermions to discuss the classic Tomonaga problem. In the case of noninteracting fermions, the bosonized hamiltonian naturally splits into an O$(N)$ piece and an O$(1)$ piece. We show that in the large-N and low-energy limit, the O$(N)$ piece in the hamiltonian describes a massless relativistic boson, while the O$(1)$ piece gives rise to cubic self-interactions of the boson. At finite $N$ and high energies, the low-energy effective description breaks down and the exact bosonized hamiltonian must be used. We also comment on the connection between the Tomonaga problem and pure Yang-Mills theory on a cylinder. In the dual context of baby universes and multiple black holes in string theory, we point out that the O$(N)$ piece in our bosonized hamiltonian provides a simple understanding of the origin of two different kinds of nonperturbative O$(e^{-N})$ corrections to the black hole partition function.

hep-th↗

arXiv2006

From Gravitons to Giants

We discuss exact quantization of gravitational fluctuations in the half-BPS sector around AdS$_5 \times $S$^5$ background, using the dual super Yang-Mills theory. For this purpose we employ the recently developed techniques for exact bosonization of a finite number $N$ of fermions in terms of $N$ bosonic oscillators. An exact computation of the three-point correlation function of gravitons for finite $N$ shows that they become strongly coupled at sufficiently high energies, with an interaction that grows exponentially in $N$. We show that even at such high energies a description of the bulk physics in terms of weakly interacting particles can be constructed. The single particle states providing such a description are created by our bosonic oscillators or equivalently these are the multi-graviton states corresponding to the so-called Schur polynomials. Both represent single giant graviton states in the bulk. Multi-particle states corresponding to multi-giant gravitons are, however, different, since interactions among our bosons vanish identically, while the Schur polynomials are weakly interacting at high enough energies.

hep-th↗