Thermal transport and gravitational anomalies in Weyl semimetals.

A hand-full of recent thermal transport experiments have been interpreted as a measurement of an elusive gravitational anomaly, an exotic quantum mechanical phenomenon that is associated to strong gravitational fields, like those near black-holes. They raise the challenge to find a clear link between gravitational anomalies, that require strong gravitational fields, and condensed matter experiments, that are realized in negligable gravitational fields. Finding this link requires to go beyond a commonplace idea due to Luttinger, who noticed that thermal transport caused by a thermal gradient is analogous to transport caused by an auxiliary gravitational field. The reason is that Luttinger developed this "trick" for small gravitational fields, far from those that activate the anomaly. The failure of Luttinger idea is the open problem that I will address in my talk. I will review the different links between thermal transport and gravitational anomalies that have been suggested. I will end by discussing our own ongoing efforts to understand how Luttinger's trick can succeed in strong gravitational fields.