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

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.

Comments: 27 pages; v2 minor changes in sec. 5 and discussion improved in secs. 6 and 7, references added, version to appear in JHEP