Nonanalyticity of the nonabelian five-dimensional Chern-Simons term

TL;DR

This paper investigates the nonanalytic behavior of the five-dimensional nonabelian Chern-Simons term at finite temperature using perturbative and non-perturbative methods, revealing noncommuting limits in the photon self-energy.

Contribution

It demonstrates the nonanalyticity of the nonabelian five-dimensional Chern-Simons term at finite temperature without regularization, highlighting the noncommuting limits of static and long wavelength regimes.

Findings

Nonanalyticity of the photon self-energy at finite temperature.

Noncommuting static and long wavelength limits.

Tensorial structure preserved in both limits.

Abstract

In this work, we study the behavior of the nonabelian five-dimensional Chern-Simons term at finite temperature regime in order to 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 $(k_0=0,\vec k\rightarrow 0)$ and the long wavelength limit $(k_0\rightarrow 0,\vec k= 0)$, while its tensorial structure holds in both limits.