Thermal transport in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>T</mml:mi><mml:mover accent="true"><mml:mi>T</mml:mi><mml:mo stretchy="false">¯</mml:mo></mml:mover></mml:math>-deformed conformal field theories: From integrability to holography
Marko Medenjak, Giuseppe Policastro, Takato Yoshimura
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 $T\overline{T}$, 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 nonequilibrium steady states, and calculate the Drude weights. Our analysis reveals that all of these quantities satisfy universal formulae regardless of the underlying CFT, thereby generalizing the universal formulas for these quantities in pure CFTs. We also compute the exact momentum diffusion constant using the integrability-based method and confirm that it agrees with the conformal perturbation. These fundamental physical insights have important consequences for our understanding of the $T\overline{T}$-deformed CFTs. First of all, they provide the first check of the $T\overline{T}$-deformed ${\mathrm{AdS}}_{3}/{\mathrm{CFT}}_{2}$ correspondence from the dynamical standpoint. And second, we are able to identify a remarkable connection between the $T\overline{T}$-deformed CFTs and reversible cellular automata.