# HTL effective action of topologically massive gluons in 3+1 dimensions

## TL;DR

This paper derives an effective action for soft gluons in a topologically massive non-Abelian gauge theory at finite temperature, highlighting the role of gluon mass in thermal perturbative analysis.

## Contribution

It constructs the HTL effective action for topologically massive gluons, incorporating the effects of gluon mass due to a topological term in thermal field theory.

## Key findings

- Gluons acquire mass through the topological term, affecting thermal behavior.
- Infrared cutoff due to gluon mass allows perturbative analysis of color diffusion and conductivity.
- Effective action captures the influence of massive gluons on thermal gluon dynamics.

## Abstract

We construct an effective action for "soft" gluons by integrating out hard thermal modes of topologically massive vector bosons at one loop order. The loop carrying hard gluons (momentum $\sim T$) are known as hard thermal loop (HTL). The gluons are massive in the non-Abelian topologically massive model (TMM) due to a quadratic coupling $B\wedge F$ where a 2-form field $B$ is coupled quadratically with the field strength $F$ of Yang-Mills (YM) field. The mass of the gluons plays an important role in the perturbative analysis of thermal field theory. Due to the presence of this infrared cut-off in the model, the color diffusion constant and conductivity can be analyzed in perturbative regime.