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arXiv:2010.15813 · Physical review. D/Physical review. D.

Thermal transport in TT¯ -deformed conformal field theories: From integrability to holography

Marko Medenjak, Giuseppe Policastro, Takato Yoshimura

Published Mar 22, 2021• 25 citations
arXivHTMLPDF

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.

DOI
10.1103/physrevd.103.066012

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We consider the out-of-equilibrium transport in TT[over ¯]-deformed (1+1)-dimension conformal field theories (CFTs). The theories admit two disparate approaches, integrability and holography, which we make full use of in order to compute the transport quantities, such as the exact nonequilibrium steady state currents. We find perfect agreements between the results obtained from these two methods, which serve as nontrivial checks of the TT[over ¯]-deformed holographic correspondence from the dynamical standpoint. It turns out that integrability also allows us to compute the momentum diffusion, which is given by a universal formula. We also remark on an intriguing connection between the TT[over ¯]-deformed CFTs and reversible cellular automata.
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Modular covariance and uniqueness of JT‾ J\overline{T} JT deformed CFTs
A bstract We study families of two dimensional quantum field theories, labeled by a dimensionful parameter μ , that contain a holomorphic conserved U(1) current J ( z ). We assume that these theories can be consistently defined on a torus, so their partition sum, with a chemical potential for the charge that couples to J , is modular covariant. We further require that in these theories, the energy of a state at finite μ is a function only of μ , and of the energy, momentum and charge of the corresponding state at μ = 0, where the theory becomes conformal. We show that under these conditions, the torus partition sum of the theory at μ = 0 uniquely determines the partition sum (and thus the spectrum) of the perturbed theory, to all orders in μ , to be that of a μJT‾ \mu J\overline{T} μJT μ J T ¯ deformed conformal field theory (CFT). We derive a flow equation for the JT‾ J\overline{T} JT J T ¯ deformed partition sum, and use it to study non-perturbative effects. We find non-perturbative ambiguities for any non-zero value of μ , and comment on their possible relations to holography.
Recently, remarkably simple exact results were presented about the dynamics of heat transport in the local Luttinger model for nonequilibrium initial states defined by position-dependent temperature profiles. We present mathematical details on how these results were obtained. We also give an alternative derivation using only algebraic relations involving the energy-momentum tensor which hold true in any unitary conformal field theory (CFT). This establishes a simple universal correspondence between initial temperature profiles and the resulting heat-wave propagation in CFT. We extend these results to larger classes of nonequilibrium states. It is proposed that such universal CFT relations provide benchmarks to identify nonuniversal properties of nonequilibrium dynamics in other models.
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