Definition of Chern-Simons Terms in Thermal QED_3 Revisited

TL;DR

This paper revisits the correct definition of the Chern-Simons term in thermal QED_3, providing two derivations that confirm previous cohomological results and clarify gauge transformation behavior.

Contribution

It introduces two compact derivations of the Chern-Simons term in thermal QED_3, validating earlier cohomology findings and supporting a heuristic approach.

Findings

Corrected Chern-Simons term definition in thermal QED_3

Agreement with cohomology-based conclusions

Clarification of large gauge transformation behavior

Abstract

We present two compact derivations of the correct definition of the Chern-Simons term in the topologically non trivial context of thermal $QED_3$. One is based on a transgression descent from a D=4 background connection, the other on embedding the abelian model in SU(2). The results agree with earlier cohomology conclusions and can be also used to justify a recent simple heuristic approach. The correction to the naive Chern-Simons term, and its behavior under large gauge transformations are displayed.