Central Charges and Effective Action at Finite Temperature and Density

TL;DR

This paper investigates the current algebra and central charge in gauge theories like QCD at finite temperature and density, revealing that the central charge depends on coupling but may be affected by thermal and density effects in four dimensions.

Contribution

It provides an explicit current algebra for the massless Thirring model at finite temperature and density and discusses implications for QCD in four dimensions.

Findings

Central charge depends only on coupling in the Thirring model.

Finite temperature and density do not alter the central charge in the 2D model.

Potential modifications of central charge in 4D QCD due to thermal effects.

Abstract

The current algebra for gauge theories like QCD at finite temperature and density is studied. We start considering, the massless Thirring model at finite temperature and density, finding an explicit expression for the current algebra. The central charge only depends on the coupling constant and there are not new effects due to temperature and density. From this calculation, we argue how to compute the central charge for $QCD_4$ and we argue why the central charge in four dimensions could be modified by finite temperature and density.