Cutoff $\mathrm{Ad}{\mathrm{S}}_3$ versus $\mathrm{T}\bar{\mathrm{T}}$ $\mathrm{CF}{\mathrm{T}}_2$ in the large central charge sector: correlators of energy-momentum tensor

Abstract

In this article we probe the proposed holographic duality between $T\bar{T}$ deformed two dimensional conformal field theory and the gravity theory of $\mathrm{Ad}{\mathrm{S}}_3$ with a Dirichlet cutoff by computing correlators of energy-momentum tensor. We focus on the large central charge sector of the $T\bar{T}$ CFT in a Euclidean plane and in a sphere, and compute the correlators of energy-momentum tensor using an operator identity promoted from the classical trace relation. The result agrees with a computation of classical pure gravity in $\mathrm{Ad}{\mathrm{S}}_3$ with the corresponding cutoff surface, given a holographic dictionary which identifies gravity parameters with $T\bar{T}$ CFT parameters.

Updated May 17: typos corrected, reference list expanded, computation of two point correlators in hyperbolic space added. Updated Aug 26: edited for submission to journal

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Cited by in corpus (18)

• Correlation functions of the CFTs on torus with $T\bar{T}$ deformation
• Geometrizing $T\bar{T}$
• Geometric formulation of generalized root-$T\bar{T}$ deformations
• Correlation Functions in $\text{T}\bar{\text{T}}$-deformed Conformal Field Theories
• Geometrizing non-relativistic bilinear deformations
• Holographic torus correlators of stress tensor in $Ad{S}_3/CF{T}_2$
• $T\bar{T}$-flow effects on torus partition functions
• End of the World Brane meets $T\bar{T}$
• $T\bar{T}/J\bar{T}$-deformed WZW models from Chern-Simons AdS${}_3$ gravity with mixed boundary conditions
• Surface charges in Chern-Simons gravity with $T\bar{T}$ deformation
• Entanglement Entropy and Modular Hamiltonian of free fermion with deformations on a torus
• One-loop partition functions in $T\overline{T}$-deformed AdS${}_3$
• Supersymmetric black holes and $T\bar{T}$ deformation
• Holographic $T\bar{T}$ deformation of the entanglement entropy in (A)dS${}_3$/CFT${}_2$
• Holographic boundary conformal field theory with $T\bar{T}$ deformation
• Systematic approach to correlators in $T\bar{T}$ deformed CFTs
• Correlation Functions in $\text{T}\bar{\text{T}}$-deformed Theories on the Torus
• Note on higher-point correlation functions of the $T\bar{T}$ or $J\bar{T}$ deformed CFTs