Exploiting duality in a toy model of QCD at non-zero temperature and chemical potential: the massive Thirring model, sine-Gordon model and Coulomb gases

TL;DR

This paper explores how duality between models like the massive Thirring, sine-Gordon, and Coulomb gases simplifies calculations in a 1+1 dimensional setting at finite temperature and chemical potential, providing insights relevant to QCD.

Contribution

It demonstrates the use of duality to facilitate calculations in a toy model of QCD, highlighting parallels and simplifying complex computations.

Findings

Duality links the massive Thirring and sine-Gordon models.

High-temperature behavior relates to an exactly solvable Coulomb gas.

Simplifies the calculation of physical quantities like transport coefficients.

Abstract

We focus on the massive Thirring model in 1+1 dimensions at finite temperature and non-zero chemical potential, and comment on some parallels between this model and QCD. In QCD, calculations of physical quantities such as transport coefficients are extremely difficult. In the massive Thirring model, similar calculations are greatly simplified by exploiting the duality which exists with the sine-Gordon model and its relation, at high temperature, to the exactly solvable classical Coulomb gas on the line.