Induced higher-derivative Lorentz-violating Chern-Simons term at finite temperature

TL;DR

This paper investigates how a higher-derivative Lorentz-violating Chern-Simons term is generated at different temperatures, showing it exists at zero temperature but vanishes at infinite temperature, and examines its gauge invariance.

Contribution

It provides the first detailed analysis of the finite-temperature behavior of the higher-derivative Lorentz-violating Chern-Simons term using derivative expansion and Matsubara formalism.

Findings

The induced higher-derivative Chern-Simons term is nonzero at zero temperature.

The coefficients of the induced term vanish at infinite temperature.

The higher-derivative and conventional Chern-Simons terms are invariant under large gauge transformations.

Abstract

In this work, we analyze the generation of the higher-derivative Lorentz-violating Chern-Simons term at zero temperature and at finite temperature. We use the method of derivative expansion and the Matsubara formalism in order to consider the finite temperature effects. The results show that at zero temperature the induced higher-derivative Chern-Simons term is nonzero; in contrast, when the temperature reaches infinity, the coefficients of the induced term vanish. In addition, we also briefly study the question of large gauge invariance of this higher-derivative term as we as the conventional Chern-Simons term. We compute the exact induced action for both terms at finite temperature, however, in a particular gauge field background, and observe that they are, in fact, invariant under large gauge transformation.