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

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.