QCD-like theories at nonzero temperature and density

TL;DR

This paper explores the phase structure of QCD-like theories at finite temperature and density using a NJL model, revealing insights into chiral and deconfinement transitions, diquark condensation, and Casimir scaling.

Contribution

It introduces a unified framework to analyze phase transitions in QCD-like theories with various gauge groups and quark representations, including a new expression for Polyakov loop expectations.

Findings

Critical temperature of chiral transition is higher than deconfinement temperature.

Diquark BEC phase transition occurs at half the diquark mass.

Polyakov loop expectation value expression enables Casimir scaling analysis.

Abstract

We investigate the properties of hot and/or dense matter in QCD-like theories with quarks in a (pseudo)real representation of the gauge group using the Nambu-Jona-Lasinio model. The gauge dynamics is modeled using a simple lattice spin model with nearest-neighbor interactions. We first keep our discussion as general as possible, and only later focus on theories with adjoint quarks of two or three colors. Calculating the phase diagram in the plane of temperature and quark chemical potential, it is qualitatively confirmed that the critical temperature of the chiral phase transition is much higher than the deconfinement transition temperature. At a chemical potential equal to half of the diquark mass in the vacuum, a diquark Bose-Einstein condensation (BEC) phase transition occurs. In the two-color case, a Ginzburg-Landau expansion is used to study the tetracritical behavior around the intersection point of the deconfinement and BEC transition lines, which are both of second order. We obtain a compact expression for the expectation value of the Polyakov loop in an arbitrary representation of the gauge group (for any number of colors), which allows us to study Casimir scaling at both nonzero temperature and chemical potential.