The Chiral Heat Effect

TL;DR

The paper identifies a Chiral Heat Effect (CHE) in a $(3+1)$-dimensional fermionic theory with a chiral (and mixed gauge-gravitational) anomaly on curved space, where a heat current flows perpendicular to a temperature gradient. By introducing a topological $\theta(t,\vec{x})$ term coupled to the Pontryagin density and relating thermal gradients to metric fluctuations via Luttinger’s prescription, the authors derive a transverse, anomaly-driven thermal response that persists even on flat space, including nonlinear contributions such as $\langle J^T_y \rangle \propto \partial_z \theta \; \partial_x^2 \delta g_{tx}$ and, for time-dependent $\theta$, $\langle J^T_z \rangle$ terms. They also formulate a torsional analogue through the Nieh-Yan term, predicting a momentum current tied to torsion flux and a boundary gravitational Chern-Simons response with Hall viscosity $\eta_H = \hbar/(8\pi \ell^2)$. The authors discuss holographic realizations in AdS/CFT (D3/D7 and Sakai-Sugimoto setups) and argue that CHE should persist at strong coupling, outlining concrete directions for holographic computations of the thermal current. Overall, CHE extends CME-like transport to thermal transport and unveils a topological mechanism for heat flow in quantum field theories.

Abstract

We consider the thermal response of a (3+1)-dimensional theory with a chiral anomaly on a curved space motivated by the chiral magnetic effect. We find a new phenomenon, called the chiral heat effect, such that the thermal current is induced transverse to a gradient of the temperature even on a flat space. This effect is expected to be observed in QCD experiment as well as the chiral magnetic effect. We study a similar topological effect on the spacetime with a torsion. A holographic construction is also discussed with the D3/D7 and the Sakai-Sugimoto models.