Induced Lorentz-violating terms at finite temperature

TL;DR

This paper investigates how Lorentz-violating terms are induced at finite temperature through quantum corrections, revealing temperature-dependent behaviors of these terms using advanced theoretical methods.

Contribution

It provides a detailed calculation of Lorentz-violating terms at finite temperature, including the temperature dependence of the Chern-Simons and higher-derivative terms, using derivative expansion and Matsubara formalism.

Findings

Chern-Simons term is nonzero only at finite temperature.

Higher-derivative term is finite at zero temperature and vanishes at high temperature.

A higher-derivative Chern-Simons term is found but vanishes asymptotically.

Abstract

We study the radiatively induced Lorentz-violating terms at finite temperature, namely, the higher-derivative term and the Chern-Simons term. These terms are induced by integrating out the fermions coupled to the coefficient $g^{\kappa\mu\nu}$. The calculation of the resulting expressions is performed by using the derivative expansion and the Matsubara formalism. The Chern-Simons terms is nonzero only at finite temperature, whereas the higher-derivative term is finite at zero temperature, however, it goes to zero as the temperature grows to infinity. We also obtain a higher-derivative Chern-Simons term, nevertheless, it vanishes asymptotically.