Moving the CFT into the bulk with $T\bar T$

TL;DR

This paper explores the holographic dual of the solvable $T\bar T$ deformation of 2D CFTs, showing it corresponds to a geometric cutoff in AdS space and confirming the duality through exact matches in physical quantities.

Contribution

It proposes a geometric interpretation of the $T\bar T$ deformation as a finite radial cutoff in AdS and derives an exact RG flow equation matching gravity's Hamilton-Jacobi equation.

Findings

Precise match of signal speed, energy spectrum, and thermodynamics between CFT and gravity sides.

Derivation of an exact RG flow equation for the deformed theory's effective action.

Identification of the $T\bar T$ deformation with a finite cutoff in holographic duality.

Abstract

Recent work by Zamolodchikov and others has uncovered a solvable irrelevant deformation of general 2D CFTs, defined by turning on the dimension 4 operator $T \bar T$, the product of the left- and right-moving stress tensor. We propose that in the holographic dual, this deformation represents a geometric cutoff that removes the asymptotic region of AdS and places the QFT on a Dirichlet wall at finite radial distance $r = r_c$ in the bulk. As a quantitative check of the proposed duality, we compute the signal propagation speed, energy spectrum, and thermodynamic relations on both sides. In all cases, we obtain a precise match. We derive an exact RG flow equation for the metric dependence of the effective action of the $T \bar T$ deformed theory, and find that it coincides with the Hamilton-Jacobi equation that governs the radial evolution of the classical gravity action in AdS.