Non-analyticity of the induced Carroll-Field-Jackiw term at finite temperature

Abstract

In this paper, we discuss the behavior of the Carroll-Field-Jackiw (CFJ) coefficient arising due to integration over massive fermions, and the modification suffered by its topological structure in the finite-temperature case. Our study is based on the imaginary time formalism and summation over the Matsubara frequencies. We demonstrate that the self-energy of photon is non-analytic for the small- limit, i.e., the static limit and the long-wavelength limit do not commute, while the tensorial structure of the CFJ term holds in both limits.