Gauge Invariance and Effective Actions in D=3 at Finite Temperature

TL;DR

This paper provides an elementary derivation of the exact Chern-Simons effective action in three-dimensional QED at finite temperature, extending it to related models and more general gauge configurations.

Contribution

It offers a simplified derivation of the induced Chern-Simons action and extends the results to mixed terms, flux dependence, and higher-order contributions in gauge fields.

Findings

Derived the exact induced Chern-Simons action at finite temperature.

Extended results to mixed Chern-Simons terms in superconductivity models.

Analyzed flux dependence and higher-order gauge field contributions.

Abstract

For background gauge field configurations reducible to the form Amu = (A3, A(x)) where A3 is a constant, we provide an elementary derivation of the recently obtained result for the exact induced Chern-Simons (CS) effective action in QED3 at finite temperature. The method allows us to extend the result in several useful ways: to obtain the analogous result for the `mixed' CS term in the Dorey-Mavromatos model of parity-conserving planar superconductivity, thereby justifying their argument for flux quantization in the model; to the induced CS term for a tau-dependent flux; and to the term of second order in A(x) (and all orders in A3) in the effective action.