Parity breaking in 2+1 dimensions and finite temperature

TL;DR

This paper develops a derivative expansion method to compute the effective action of 2+1-dimensional fermions at finite temperature, capturing gauge and parity symmetries and anomalies, and reproducing known limits and exact results.

Contribution

It introduces a gauge- and parity-preserving derivative expansion for the effective action of fermions in 2+1 dimensions at finite temperature, including non-Abelian backgrounds.

Findings

Successfully computes the real and imaginary parts of the effective action.

Reproduces known limits such as massless fermions and zero temperature.

Maintains gauge invariance and parity symmetry in the expansion.

Abstract

An expansion in the number of spatial covariant derivatives is carried out to compute the $\zeta$-function regularized effective action of 2+1-dimensional fermions at finite temperature in an arbitrary non-Abelian background. The real and imaginary parts of the Euclidean effective action are computed up to terms which are ultraviolet finite. The expansion used preserves gauge and parity symmetries and the correct multivaluation under large gauge transformations as well as the correct parity anomaly are reproduced. The result is shown to correctly reproduce known limiting cases, such as massless fermions, zero temperature, and weak fields as well as exact results for some Abelian configurations. Its connection with chiral symmetry is discussed.