Nonanalyticity of the non-Abelian five-dimensional Chern-Simons term

Abstract

In this work, we study the behavior of the non-Abelian five-dimensional Chern-Simons term at finite-temperature regime in order to verify the possible non-analyticity. We employ two methods, a perturbative and a non-perturbative one. No scheme of regularization is needed, and we verify the non-analyticity of the self-energy of the photon in the origin of momentum space by two conditions that do not commute, namely, the static limit and the long-wavelength limit , while its tensorial structure holds in both limits.