Parity violating gravitational response and anomalous constitutive relations

TL;DR

This paper calculates the parity-violating gravitational response of Weyl fermions, revealing new invariant contributions to the anomalous partition function and providing insights into time-dependent anomaly-driven phenomena.

Contribution

It introduces a detailed tensorial structure of the gravitational response function and uncovers a previously unknown invariant term at third derivative order.

Findings

Identifies two key functions parametrizing the energy-momentum tensor.

Links zero frequency limit to anomalous constitutive relations.

Constructs a new invariant contribution to the parity-odd partition function.

Abstract

We compute the parity violating part of the time-dependent gravitational response function of an ideal gas of Weyl fermions up to third order in the derivative expansion and give its full tensorial structure. Our main results are two functions that parametrize the energy-momentum tensor in terms of gauge-invariant combinations of vector and tensor metric perturbations. The zero frequency limit of these functions is related with the anomalous constitutive relations and with the full anomalous partition function in the presence of gauge and mixed anomalies. In particular, our results imply the existence of a previously unknown invariant contribution to the parity-odd partition function at third derivative order that we explicitly construct. Beyond the static limit, the gravitational response function may provide valuable insights into time-dependent phenomena driven by anomalies.