Torsional response of relativistic fermions in $2+1$ dimensions

TL;DR

This paper investigates how torsion affects the properties of relativistic fermions in 2+1 dimensions, revealing connections to Hall viscosity and parity violation, and develops a consistent entropy current in equilibrium.

Contribution

It provides a detailed analysis of the torsional response of relativistic fermions, including the energy-momentum tensor, susceptibilities, and entropy current, in 2+1 dimensions.

Findings

Energy-momentum tensor reproduces Hall viscosity.

Identifies parity-violating terms due to torsion.

Constructs an entropy current with zero entropy production.

Abstract

We consider the equilibrium partition function of an ideal gas of Dirac fermions minimally coupled to torsion in $2+1$ dimensions. We show that the energy-momentum tensor reproduces the Hall viscosity and other parity violating terms of first order in the torsion. We also consider the modifications of the constitutive relations, and classify the corresponding susceptibilities. An entropy current consistent with zero production of entropy in equilibrium is constructed.