Thermal backflow in CFTs

Abstract

Reprinted with permission from the American Physical Society: Physical Review D 95, 025022 c (2017) by the American Physical Society. Readers may view, browse, and/or download material for temporary copying purposes only, provided these uses are for noncommercial personal purposes. Except as provided by law, this material may not be further reproduced, distributed, transmitted, modied, adapted, performed, displayed, published, or sold in whole or part, without prior written permission from the American Physical Society.Additional information: Use policyThe full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-prot purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details. We study the thermal transport properties of general conformal field theories (CFTs) on curved spacetimes in the leading order viscous hydrodynamic limit. At the level of linear response, we show that the thermal transport is governed by a system of forced linearized Navier-Stokes equations on a curved space. Our setup includes CFTs in flat spacetime that have been deformed by spatially dependent and periodic local temperature variations or strains that have been applied to the CFT, and hence is relevant to CFTs arising in condensed matter systems at zero charge density. We provide specific examples of deformations which lead to thermal backflow driven by a dc source: that is, the thermal currents locally flow in the opposite direction to the applied dc thermal source. We also consider thermal transport for relativistic quantum field theories that are not conformally invariant.

Diffusion in inhomogeneous media

“…However, motivated by recent experimental progress [3][4][5], there has been considerable theoretical work using hydrodynamics to study thermoelectric transport [2,[6][7][8][9][10][11][12][13][14][15][16][17][18] and it is therefore of interest to see how our general results on diffusion manifest themselves in this particular context. More specifically, we will study this within the context of relativistic hydrodynamics, describing the hydrodynamic limit of a relativistic quantum field theory.…”

“…In this spirit, the hydrodynamic limit of a class of field theories which have been deformed by certain scalar operators was analyzed in [7]. Subsequently, the universal class of deformations which involve adding spatially dependent sources for the stress tensor were studied in [14]. Since the stress tensor of the field theory couples to the spacetime metric, the deformations studied in [14] are equivalent to studying the hydrodynamic limit of the quantum field theory on a curved spacetime manifold.…”

“…Subsequently, the universal class of deformations which involve adding spatially dependent sources for the stress tensor were studied in [14]. Since the stress tensor of the field theory couples to the spacetime metric, the deformations studied in [14] are equivalent to studying the hydrodynamic limit of the quantum field theory on a curved spacetime manifold. The spacetime metric is taken to have a timelike Killing vector in order to discuss thermal equilibrium.…”

“…In this paper we extend the analysis of [14] to cover relativistic quantum field theories which have a conserved Uð1Þ symmetry. As in [14] we can consider the field theory to live on a static, curved manifold.…”

“…Then, while spatial momentum will, generically, no longer be conserved, energy still will be. It may be possible to experimentally realize the deformations studied in [14] in real materials, such as strained graphene [21][22][23].…”