Thermal transport, geometry, and anomalies

TL;DR

This paper reviews the connections between thermal transport phenomena, space-time geometry, and quantum anomalies, emphasizing insights from condensed matter physics and high-energy theories, and discusses recent experimental progress and open challenges.

Contribution

It synthesizes ideas linking thermal transport, space-time geometry, and quantum anomalies, highlighting interdisciplinary advances and proposing future research directions.

Findings

Relation between thermal transport and gravitational anomalies

Emergence of geometric concepts in condensed matter systems

Identification of open problems in thermal transport and anomalies

Abstract

The relation between thermal transport and gravity was highlighted in the seminal work by Luttinger in 1964, and has been extensively developed to understand thermal transport, most notably the thermal Hall effect. Here we review the novel concepts that relate thermal transport, the geometry of space-time and quantum field theory anomalies. We give emphasis to the cross-pollination between emergent ideas in condensed matter, notably Weyl and Dirac semimetals, and the understanding of gravitational and scale anomalies stemming from high-energy physics. We finish by relating to recent experimental advances and presenting a perspective of several open problems.