Quantum gravity in a finite region of spacetime is conjectured to be dual conformal field theory (CFT) deformed by the irrelevant operator TT[over ¯]. We test this conjecture with entanglement entropy, which sensitive ultraviolet physics on boundary, while also probing bulk geometry. find that entropy for an entangling surface consisting two antipodal points sphere and precisely matches Ryu-Takayanagi formula applied consistent McGough et al. consider one-parameter family conical entropies,...

A bstract 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 AdS +1 a finite radial cut-off. then demonstrate how equation can be independently derived from regularization procedure defining operators through local Callan-Symanzik Finally, we show that functions, modulo bulk-counterterm contributions, reproduced...

A bstract We obtain microstates accounting for the Gibbons-Hawking entropy in dS 3 , along with a subleading logarithmic correction, from solvable T $$ \overline{T} <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mover> <mml:mi>T</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> </mml:math> + Λ 2 deformation of seed CFT sparse light spectrum. The arise as dressed states near dimension ∆ = c/ 6, associated Hawking-Page transition; they dominate real spectrum deformed theory. exhibit an...

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

A bstract The $$ T\overline{T} <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>T</mml:mi> <mml:mover> <mml:mo>¯</mml:mo> </mml:mover> </mml:math> + Λ 2 deformation of a Holographic CFT on cylinder (or torus in Euclidean signature) inhabits the stretched cosmological horizon dS 3 when parameter is tuned to particular value. I will describe how this insight allows us compute entropy cosmic including logarithmic correction.

We calculate quantum corrections to holographic entanglement entropy in the proposed duality between $$ T\overline{T} -deformed 2D CFTs and gravity AdS3 with a finite cutoff. first establish dictionary two theories by mapping flow equation of deformed CFT bulk Wheeler-DeWitt equation. The latter reduces an ordinary differential for sphere partition function, which we solve find entangling surface consisting antipodal points on sphere. inverse central charge expansion yields expectation value...

Recently proposed double trace deformations of large $N$ holographic CFTs in four dimensions define a one parameter family quantum field theories, which are interpreted the bulk dual as living on successive finite radius hypersurfaces. The transformation variables that turns equation defining deformation dimensional CFT by such operators into expression for radial ADM Hamiltonian is found. This prescription clarifies role various functions background fields appear flow deformed CFT, and also...

We propose a generalisation of the $T \bar{T}$ deformation to curved spaces by defining, and solving, suitable flow equation for partition function. provide evidence it is well-defined at quantum level. This proposal identifies, any CFT, deformed function certain wavefunction 3d gravity. connection, true $c$, not holographic duality --- theory "fake bulk." however emphasise that this reduces known connection in classical limit. Concretely, means solves exactly just one global equation,...

A bstract We consider the $$ T\overline{T} <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>T</mml:mi> <mml:mover> <mml:mo>¯</mml:mo> </mml:mover> </mml:math> deformation of two dimensional Yang-Mills theory on general curved backgrounds. compute deformed partition function through an integral transformation over frame fields weighted by a Gaussian kernel. show that this satisfies flow equation which has been derived previously in literature, now holds connect ambiguities...

The quantum renormalization group (QRG) is a realization of holography through coarse-graining prescription that maps the beta functions field theory thought to live on ``boundary'' some space holographic actions in ``bulk'' this space. A consistency condition will be proposed translates into general covariance gravitational $D+1$ dimensional bulk. This emerges from application QRG planar matrix living $D$ boundary. particular form Wess-Zumino generating functional boundary needs satisfy. In...

A bstract We construct a particular flow in the space of 2D Euclidean QFTs on torus, which we argue is dual to class solutions 3D gravity with conformal boundary conditions. This new comes from Legendre transform kernel implements T $$ \overline{T} <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mover> <mml:mi>T</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> </mml:math> deformation, and motivated by need for conditions be elliptic, i.e. that they have well-defined propagators metric...

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

A bstract The Holographic Wess-Zumino (HWZ) consistency condition is shown through a step by mapping of renormalization group flows to Hamiltonian systems, lead the anomaly. This codifies how energy scale, when treated as emergent bulk direction in theories, put on equal footing other directions space field theory inhabits. So, this defining feature theories possessing local duals. In four dimensional conformal and c anomaly coefficients are equated, seen property which possess General...

Shape dynamics is a 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 takes spatial invariance Weyl as the fundamental associated gravitational field. Since area event horizon black hole transforms under generic transformation, there has been some doubt that one can speak sensibly about thermodynamics holes dynamics. The purpose this paper...

In this note, we show that the noncovariant metric boundary term obtained from nonlinear sigma model worldsheet derivation of bulk off-shell sphere partition function is closely related to Einstein in Gamma-Gamma action. fact, when expressed terms trace extrinsic curvature tensor, illustrate has one-half coefficient Gibbons-Hawking-York required such total (bulk plus boundary) classical action a well-posed variational principle with Dirichlet conditions.

A bstract We show the $$ T\overline{T} <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>T</mml:mi> <mml:mover> <mml:mo>¯</mml:mo> </mml:mover> </mml:math> deformation of two-dimensional quantum field theories is equivalent to replacing spacetime dependence fields with on indices infinitely large matrices. how this correspondence explains CDD phase dressing S -matrix and general formula for arbitrary correlation functions. also describe Moyal self-dual gravity a theory...

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

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

In general relativity, the double null foliation is one for which $d$-dimensional spacetime foliated by two families of intersecting hyper surfaces (i.e. whose normal vectors are null) $(d-1)$ dimensions. Their intersection at space like dimension $(d-2)$. This means that leaves this dimensions lower than located looking bundles light rays going into, and emanating from them. Using foliation, we present a reformulation theory makes explicit true dynamical degrees freedom. accompanied making...

I will show how the flow triggered by deforming two-dimensional conformal field theories on a torus TT¯ operator is identical to evolution generated (radial) quantum Shape Hamiltonian in 2 + 1 dimensions. discuss gauge invariances of Dynamics, i.e., volume-preserving invariance and diffeomorphism along slices constant radius are realized as Ward identities deformed theory. also comment about relationship between reduction shape space gravity side solvability irrelevant deformation theory

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