Cutoff AdS$_3$ versus the $T\bar{T}$ deformation

TL;DR

This paper explores the relationship between $Tar{T}$-deformed 2D CFTs and AdS$_3$ with a finite cutoff, matching correlation functions and predicting loop corrections in the bulk gravity theory.

Contribution

It provides a detailed perturbative comparison of correlation functions between $Tar{T}$-deformed CFTs and bulk AdS$_3$ gravity, including matter fields and loop effects.

Findings

Successful match of stress tensor correlators at large central charge

Predictions for bulk loop corrections from the deformed CFT

Necessity of double trace operators to reproduce bulk two-point functions

Abstract

A recent proposal relates two dimensional holographic conformal field theories deformed by the integrable $T\bar{T}$ flow to AdS$_3$ with a finite radial cutoff. We investigate this proposal by studying perturbative correlation functions on the two sides. For low point correlators of the stress tensor, we successfully match the deformed CFT results at large central charge to bulk results obtained in classical pure gravity. The deformed CFT also provides definite predictions for loop corrections in the bulk. We then include matter fields in the bulk. To reproduce the classical bulk two-point function of a scalar operator we show that the deformed CFT needs to be augmented with double trace scalar operators, with the $T\bar{T}$ operator yielding corrections corresponding to loops in the bulk.