arXiv subjects

Vasudev Shyam

Publications and source records attributed to Vasudev Shyam.

34 records · Page 2Linked to original sources

arXiv2019

A $T \bar{T}$ Deformation for Curved Spacetimes from 3d Gravity

We propose a generalisation of the $T \bar{T}$ deformation to curved spaces by defining, and solving, a suitable flow equation for the partition function. We provide evidence it is well-defined at the quantum level. This proposal identifies, for any CFT, the $T \bar{T}$ deformed partition function and a certain wavefunction of 3d quantum gravity. This connection, true for any $c$, is not a holographic duality --- the 3d theory is a "fake bulk." We however emphasise that this reduces to the known holographic connection in the classical limit. Concretely, this means the deformed partition function solves exactly not just one global equation, defining the $T \bar{T}$ flow, but in fact a local Wheeler-de Witt equation, relating the $T \bar{T}$ operator to the trace of the stress tensor. This also immediately suggests a version of the $T \bar{T}$ deformation with locally varying deformation parameter. We flesh out the connection to 3d gravity, showing that the partition function of the deformed theory is precisely a 3d gravity path integral. In particular, in the classical limit, this path integral reproduces the holographic picture of Dirichlet boundary conditions at a finite radius and mixed boundary conditions at the asymptotic boundary. Further, we reproduce known results in the flat space limit, as well as the large $c$ $S^2$ partition function, and conjecture an answer for the finite $c$ $S^2$ partition function.

hep-th↗

arXiv2019

Sphere partition functions and cut-off AdS

We consider sphere partition functions of TT deformed large N conformal field theories in d=2,3,4,5 and 6 dimensions, computed using the flow equation. These are shown to non-perturbatively match with bulk computations of $AdS_{d+1}$ with a finite radial cut-off. We then demonstrate how the flow equation can be independently derived from a regularization procedure in defining TT operators through a local Callan-Symanzik equation. Finally, we show that the sphere partition functions, modulo bulk-counterterm contributions, can be reproduced from Wheeler-DeWitt wave functions.

hep-th↗

arXiv2018

Finite Cutoff AdS$_{5}$ Holography and the Generalized Gradient Flow

Recently proposed double trace deformations of large $N$ holographic CFTs in four dimensions define a one parameter family of quantum field theories, which are interpreted in the bulk dual as living on successive finite radius hypersurfaces. The transformation of variables that turns the equation defining the deformation of a four dimensional large $N$ CFT by such operators into the expression for the radial ADM Hamiltonian in the bulk is found. This prescription clarifies the role of various functions of background fields that appear in the flow equation defining the deformed holographic CFT, and also their relationship to the holographic anomaly. The effect of these deformations can also be seen as triggering a generalized gradient flow for the fields of the induced gravity theory obtained from integrating out the fundamental fields of the holographic CFT. The potential for this gradient flow is found to resemble the two derivative effective action previously derived using holographic renormalization.

hep-th↗

arXiv2018

Entanglement entropy and $T \overline{T}$ deformation

Quantum gravity in a finite region of spacetime is conjectured to be dual to a conformal field theory deformed by the irrelevant operator $T \overline{T}$. We test this conjecture with entanglement entropy, which is sensitive to ultraviolet physics on the boundary while also probing the bulk geometry. We find that the entanglement entropy for an entangling surface consisting of two antipodal points on a sphere is finite and precisely matches the Ryu-Takayanagi formula applied to a finite region consistent with the conjecture of McGough, Mezei and Verlinde. We also consider a one-parameter family of conical entropies, which are finite and verify a conjecture due to Dong. Since ultraviolet divergences are local, we conclude that the $T \overline{T}$ deformation acts as an ultraviolet cutoff on the entanglement entropy. Our results support the conjecture that the $T \overline{T}$-deformed CFT is the holographic dual of a finite region of spacetime.

hep-th↗

arXiv2018

Connecting Holographic Wess--Zumino Consistency Conditions to the Holographic Anomaly

The Holographic Wess--Zumino (HWZ) consistency conditions are shown through a step by step mapping of renormalization group flows to Hamiltonian systems, to lead to the Holographic anomaly. These conditions codify how the energy scale, when treated as the emergent bulk direction in Holographic theories, is put on equal footing as the other directions of the space the field theory inhabits. So, this is a defining feature of theories possessing local Holographic bulk duals. In four dimensional Holographic conformal field theories, the $a$ and $c$ anomaly coefficients are equated, and this is seen as a defining property of theories which possess General Relativity coupled to matter as a dual. Hence, showing how the former consistency conditions leads to the latter relation between anomaly coefficients adds evidence to the claim that the HWZ conditions are a defining feature of theories possessing local gravity duals.

hep-th↗

arXiv2017

Background independent holographic dual to $T\bar{T}$ deformed CFT with large central charge in 2 dimensions

The geometerization of the renormalization group flow triggered by the $T\bar{T}$ deformation of large $c$ conformal field theories in two dimensions is presented. This entails the construction of the off shell Einstein-Hilbert action in three dimensions from said renormalization group flow. The crucial ingredient to this construction will be the encoding of general covariance in the emergent bulk theory in a very particular form of the Wess--Zumino consistency conditions. The utilisation of the local renormalization group, which requires putting the theory under consideration on an arbitrary background geometry, supplemented by the aforementioned covariance condition ensures that the whole construction is background independent.

hep-th↗

arXiv2017

General Covariance from the Quantum Renormalization Group

The Quantum renormalization group (QRG) is a realisation of holography through a coarse graining prescription that maps the beta functions of a quantum field theory thought to live on the `boundary' of some space to holographic actions in the `bulk' of this space. A consistency condition will be proposed that translates into general covariance of the gravitational theory in the $D + 1$ dimensional bulk. This emerges from the application of the QRG on a planar matrix field theory living on the $D$ dimensional boundary. This will be a particular form of the Wess--Zumino consistency condition that the generating functional of the boundary theory needs to satisfy. In the bulk, this condition forces the Poisson bracket algebra of the scalar and vector constraints of the dual gravitational theory to close in a very specific manner, namely, the manner in which the corresponding constraints of general relativity do. A number of features of the gravitational theory will be fixed as a consequence of this form of the Poisson bracket algebra. In particular, it will require the metric beta function to be of gradient form.

gr-qc↗

arXiv2016

Extending the rigidity of general relativity

We give the most general conditions to date which lead to uniqueness of the general relativistic Hamiltonian. Namely, we show that all spatially covariant generalizations of the scalar constraint which extend the standard one while remaining quadratic in the momenta are second class. Unlike previous investigations along these lines, we do not require a specific Poisson bracket algebra, and the quadratic dependence on the momenta is completely general, with an arbitrary local operator as the kinetic term.

math-ph↗

arXiv2016

Towards Black Hole Entropy in Shape Dynamics

Shape dynamics is classical theory of gravity which agrees with general relativity in many important cases, but possesses different gauge symmetries and constraints. Rather than spacetime diffeomorphism invariance, shape dynamics takes spatial diffeomorphism invariance and spatial Weyl invariance as the fundamental gauge symmetries associated with the gravitational field. Since the area of the event horizon of a black hole transforms under a generic spatial Weyl transformation, there has been some doubt that one can speak sensibly about the thermodynamics of black holes in shape dynamics. The purpose of this paper is to show that by treating the event horizon of a black hole as an interior boundary, one can recover familiar notions of black hole thermodynamics in shape dynamics and define a gauge invariant entropy that agrees with general relativity.

gr-qc↗

arXiv2015

Scale Invariance in Gravity On The Light-Front

In general relativity, the double null foliation is one for which $d$-dimensional spacetime is foliated by two families of intersecting null hyper surfaces (i.e. surfaces whose normal vectors are null) of $(d-1)$ dimensions. Their intersection is at space like surfaces of dimension $(d-2)$. This means that the leaves of this foliation are the space like surfaces of two dimensions lower than that of spacetime which are located by looking at the bundles of light rays that are going into, and emanating from them. Using this foliation, we present a reformulation of the theory which makes explicit the true dynamical degrees of freedom. This is accompanied by making manifest a hidden local conformal invariance. Revealing this local symmetry comes at the cost of preferring a parameterisation of the null hyper surfaces. More precisely, a preferred ruling of the null surfaces by their generators needs to be chosen so that the theory whose gauge symmetries are enhanced by Weyl invariance restricted to preserve the foliation, is equivalent to general relativity. I therefore find a dual theory that is locally equivalent to general relativity but possessing enhanced local gauge symmetries: Weyl local scale invariance and diffeomorphism invariance, both of which are restricted to preserve the two families of null surfaces. This theory is constructed employing the so called symmetry trading algorithm, which shall be described in detail in this essay. Alternatively, the theory can also be seen as a `phase' of a particular Scalar-Tensor theory, because it is equivalent to a particular class of configurations of a scalar field conformally coupled to general relativity.

gr-qc↗

arXiv2014

Proof of Positivity of Mass for Maximally Sliced, Asymptotically Flat Spacetimes

There exists in General Relativity an unambiguous notion of Mass associated to asymptotically flat spacetimes known as the ADM mass. The standard expression for the same is a surface integral over spatial infinity of a linear combination of spatial deriatives of the three metric adapted to a constant time spatial hypersurface evaluated at infinity. In this form however the positivity of this mass formula is not apparent, so in the following an attempt shall be made to bring this functional into a form where it's positivity is evident.

gr-qc↗

arXiv2013

On the Geometric Quantization of Canonical Gravity

One of the hardest problems to tackle in the dynamics of canonical approaches to quantum gravity is that of the Hamiltonian constraint. We investigate said problem in the context of formal geometric quantization. We study the implications of the non uniqueness in the choice of the vector field which satisfies the presymplectic equation for the Hamiltonian constraint, and study the implication of the same in the quantization of the theory. Our aim is to show that this non uniqueness in the choice of said vector field, which really stems from refoliation invariance leads to a very ambiguous notion of quantum evolution. We then investigate the case of a theory where the problem of the Hamiltonian constraint has been dealt with at the classical level, namely Shape Dynamics, and attempt to derive a time dependent Schrodinger equation for the quantum dynamics of this theory.

gr-qc↗

arXiv2013

The Canonical Lagrangian Approach To Three-Space General Relativity

We study the action for the three-space formalism of General Relativity, better known as the BFÓ (Barbour--Foster--Ó Murchadha) action, which is a square-root BSW (Baierlein--Sharp--Wheeler) action. In particular, we explore the (pre)symplectic structure by pulling it back via a Legendre map to the tangent bundle of the configuration space of this action. With it we attain the canonical Lagrangian vector field which generates the gauge transformations (3-diffeomorphisms) and the true physical evolution of the system. This vector field encapsulates all the dynamics of the system. We also discuss briefly the observables and perennials for this theory. We then present a symplectic reduction of the constrained phase space.

gr-qc↗

arXiv2012

Presymplectic Geometry And The Problem Of Time. Part 2

The Problem of Time in Quantum Gravity is analyzed from a classical presymplectic perspective. In the first part of the paper the Three Space Approach to General Relativity is introduced via the Barbour-Foster-Ó Murchadha action and the dynamics corresponding to a theory of relativistic gravity where spacetime is not an a priori requirement. We also look into the nature and physical interpretation of the constraints in this theory and compare them with those of Standard ADM General Relativity. We then study the presymplectic phase space of three space general relativity and discuss briefly the notion of observables and perennials of the system. We then move on to re-deriving the ephemeris lapse identification, and then discuss the notion of re-foliation invariance and its resolution in the conformal theory. Further, we study a new perspective of three space general relativity involving a Hamiltonian reduction of the phase space and subsequently, we discuss the path integral quantization of the same.

gr-qc↗

arXiv2012

Intrinsic Time Deparameterization of The Canonical Connection Dynamics of General Relativity

We investigate the implications of intrinsic time deparameterization on the phase space of the connection representation of canonical gravity in the form of the Ashtekar variables. We find that, much like the metric representation of this formalism, the Hamiltonian constraint now becomes a physical Hamiltonian generating evolution with respect to an intrinsic time. The complete observables for the theory are then constructed. Also, the dynamics in this formulation is cast into a classical master constraint theory.

gr-qc↗

arXiv2012

Presymplectic Geometry and the Problem of Time. Part 1

An effective mathematical framework based on Presymplectic Geometry for dealing with the "phase space picture" of timeless dynamics in General Relativity is presented. In General Relativity, the presence of the scalar Hamiltonian constraint which vanishes leads to the problem of time, which can be solved, up to an extent by adopting a timeless formalism. This has been done by Carlo Rovelli and Julian Barbour et al. In this paper we present a phase space reformulation of Barbour's theory. The Presymplectic dynamics of general totally constrained, reparametrization invariant theories is developed, then applied to Jacobi mechanics, relational particle mechanics and the dynamics of the free relativistic particle.

gr-qc↗