Nonanalyticity of the nonabelian five-dimensional Chern-Simons term

Abstract

In this work, we study the behavior of the nonabelian five-dimensional Chern-Simons term at finite temperature regime in order the verify the possible nonanalyticity. We employ two methods, a perturbative and a non-perturbative one. No scheme of regularization is needed, and we verify the nonanalyticity of the self-energy of the photon in the origin of momentum space by two conditions that do not commute, namely, the static limit (k 0 = 0, k → 0) and the long wavelength limit (k 0 → 0, k = 0), while its tensorial structure holds in both limits. The large gauge invariance method is used to obtain the effective action for the Chern-Simons at finite temperature which is invariant under nontrivial gauge transformation.