Deconfinement Transition for Quarks on a Line

TL;DR

This paper investigates the phase transition behavior of a one-dimensional quark gas with gauge interactions, revealing a first order deconfinement transition at low fundamental quark density and a third order transition at higher densities.

Contribution

It introduces a large-N analysis of phase transitions in 1D gauge theories with both adjoint and fundamental quarks, identifying the order of the transition based on quark densities.

Findings

First order deconfinement transition at low fundamental quark density.

Third order transition when fundamental and adjoint densities are comparable.

Method to distinguish phases using high winding number Polyakov loops.

Abstract

We examine the statistical mechanics of a 1-dimensional gas of both adjoint and fundamental representation quarks which interact with each other through 1+1-dimensional U(N) gauge fields. Using large-N expansion we show that, when the density of fundamental quarks is small, there is a first order phase transition at a critical temperature and adjoint quark density which can be interpreted as deconfinement. When the fundamental quark density is comparable to the adjoint quark density, the phase transition becomes a third order one. We formulate a way to distinguish the phases by considering the expectation values of high winding number Polyakov loop operators.