Second-order partition function of a non-interacting chiral fluid in 3+1 dimensions

TL;DR

This paper calculates the second-order partition function for non-interacting chiral fermions in 3+1 dimensions, highlighting the need for Pauli-Villars regularization and exploring implications for non-dissipative hydrodynamics.

Contribution

It provides the first detailed computation of the second-order partition function for chiral fermions, incorporating regularization and analyzing hydrodynamic features.

Findings

Pauli-Villars regularization is essential for consistent vacuum calculations.

The results inform non-dissipative second-order hydrodynamic relations.

Explicit form of the second-order partition function for chiral fermions.

Abstract

We compute the partition function for non-interacting chiral fermions at second order in a derivative expansion of an arbitrary time-independent gravitational and gauge background. We find that Pauli-Villars regularization of the vacuum part is needed to get consistent results. We use our results to discuss some features of the non-dissipative constitutive relations of second order hydrodynamics.