Thermal backflow in CFTs

TL;DR

This paper investigates thermal transport in conformal field theories on curved spacetimes, revealing conditions under which thermal backflow occurs due to specific deformations, with implications for condensed matter systems.

Contribution

It demonstrates how linearised Navier-Stokes equations govern thermal transport in CFTs on curved spaces and identifies conditions leading to thermal backflow in deformed CFTs.

Findings

Thermal backflow can be driven by DC sources in certain deformed CFTs.

Thermal transport is described by linearised Navier-Stokes equations on curved backgrounds.

The study extends to non-conformal relativistic quantum field theories.

Abstract

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 linearised 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.