Induced Parity Breaking Term in Arbitrary Odd Dimensions at Finite Temperature

TL;DR

This paper computes the exact parity-odd effective action for massive Dirac fermions in odd dimensions at finite temperature, revealing topological invariants' role and gauge transformation properties.

Contribution

It provides a novel exact calculation of the parity odd effective action in arbitrary odd dimensions at finite temperature, considering both Abelian and non-Abelian gauge fields.

Findings

Dependence of the effective action on topological invariants.

Gauge transformation properties linked to topological invariants and winding number.

Extension from Abelian to non-Abelian gauge groups.

Abstract

We calculate the exact parity odd part of the effective action ($\Gamma_{odd}^{2d+1}$) for massive Dirac fermions in 2d+1 dimensions at finite temperature, for a certain class of gauge field configurations. We consider first Abelian external gauge fields, and then we deal with the case of a non-Abelian gauge group containing an Abelian U(1) subgroup. For both cases, it is possible to show that the result depends on topological invariants of the gauge field configurations, and that the gauge transformation properties of $\Gamma_{odd}^{2d+1}$ depend only on those invariants and on the winding number of the gauge transformation.