The induced higher derivative Lorentz-violating Chern–Simons term at finite temperature

Abstract

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