Thermal transport in $T\bar{T}$-deformed conformal field theories: from integrability to holography

TL;DR

This paper investigates energy and momentum transport in $T\bar{T}$-deformed 2D conformal field theories using integrability and holography, revealing universal transport formulas and connections to holography and cellular automata.

Contribution

It provides the first non-equilibrium analysis of $T\bar{T}$-deformed CFTs, deriving universal transport properties and confirming their consistency with holographic duals.

Findings

Universal formulas for Drude weights and diffusion constants in $T\bar{T}$-deformed CFTs

Exact momentum diffusion constant matches conformal perturbation results

Connection established between $T\bar{T}$-deformed CFTs and reversible cellular automata

Abstract

In this paper we consider the energy and momentum transport in (1+1)-dimension conformal field theories (CFTs) that are deformed by an irrelevant operator $T\bar{T}$, using the integrability based generalized hydrodynamics, and holography. The two complementary methods allow us to study the energy and momentum transport after the in-homogeneous quench, derive the exact non-equilibrium steady states (NESS) and calculate the Drude weights and the diffusion constants. Our analysis reveals that all of these quantities satisfy universal formulae regardless of the underlying CFT, thereby generalizing the universal formulae for these quantities in pure CFTs. As a sanity check, we also confirm that the exact momentum diffusion constant agrees with the conformal perturbation. These fundamental physical insights have important consequences for our understanding of the $T\bar{T}$-deformed CFTs. First of all, they provide the first check of the $T\bar{T}$-deformed $\mathrm{AdS}_3$/$\mathrm{CFT}_2$ correspondence from the dynamical standpoint. And secondly, we are able to identify a remarkable connection between the $T\bar{T}$-deformed CFTs and reversible cellular automata.