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

In this work, we study the behavior of nonabelian five-dimensional Chern-Simons term at finite temperature regime in order to verify possible nonanalyticity. We employ two methods, a perturbative and non-perturbative one. No scheme regularization is needed, nonanalyticity self-energy photon origin momentum space by conditions that do not commute, namely, static limit $(k_0=0,\vec k\rightarrow 0)$ long wavelength $(k_0\rightarrow 0,\vec k= 0)$, while its tensorial structure holds both limits.