Nonanalyticity of the induced Carroll-Field-Jackiw term at finite temperature

TL;DR

This paper investigates the nonanalytic behavior of the Carroll-Field-Jackiw term at finite temperature, showing that different low-momentum limits do not commute, affecting the topological structure of the photon self-energy.

Contribution

It reveals the nonanalytic nature of the CFJ coefficient at finite temperature and how the static and long wavelength limits differ, impacting the topological properties.

Findings

Photon self-energy is non-analytic at small $k^{mu}$

Static and long wavelength limits do not commute

Tensorial structure of CFJ term remains valid in both limits

Abstract

In this paper, we discuss the behavior of the Carroll-Field-Jackiw (CFJ) coefficient $k^{\mu}$ 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 $k^{\mu}$ limit, i.e., the static limit $(k_0=0,\vec k\rightarrow 0)$ and the long wavelength limit $(k_0\rightarrow 0,\vec k= 0)$ do not commute, while the tensorial structure of the CFJ term holds in both limits.