Induced parity violating thermal effective action for (2+1)-dimensional fermions interacting with a non-Abelian background

TL;DR

This paper calculates the parity-violating effective action for massive fermions in 2+1 dimensions interacting with a non-Abelian gauge background at finite temperature, including static and non-static cases, ensuring gauge invariance.

Contribution

It provides explicit calculations of parity violating amplitudes up to seven-point functions and derives the exact effective action for static backgrounds, extending understanding of parity violation in non-Abelian gauge theories.

Findings

Exact effective action for static backgrounds derived.

Parity violating amplitudes computed up to seven-point functions.

Gauge invariance of the effective action established.

Abstract

We study the parity breaking effective action in 2+1 dimensions, generated, at finite temperature, by massive fermions interacting with a non-Abelian gauge background. We explicitly calculate, in the static limit, parity violating amplitudes up to the seven point function, which allows us to determine the corresponding effective actions. We derive the exact parity violating effective action when $\vec{E}=0$. When $\vec{E}\neq 0$, there are families of terms that can be determined order by order in perturbation theory. We attempt to generalize our results to non-static backgrounds through the use of time ordered exponentials and prove gauge invariance, both {\it small} and {\it large}, of the resulting effective action. We also point out some open questions that need to be further understood.