Anomaly and a QCD-like phase diagram with massive bosonic baryons

TL;DR

This paper investigates a lattice gauge theory model resembling QCD, exploring its phase diagram with three distinct phases and analyzing how the QCD anomaly influences the nature of phase transitions.

Contribution

The study introduces a lattice model with a controllable anomaly term, revealing its phase structure and the impact of the anomaly on the chiral phase transition and tricritical point.

Findings

Identified three phases: chirally broken, baryon superfluid, and symmetric phase.

Showed the anomaly significantly shifts the location of the tricritical point.

Demonstrated the model's phase diagram parallels features of real QCD.

Abstract

We study a strongly coupled $Z_2$ lattice gauge theory with two flavors of quarks, invariant under an exact $\mathrm{SU}(2)\times \mathrm{SU}(2) \times \mathrm{U}_A(1) \times \mathrm{U}_B(1)$ symmetry which is the same as QCD with two flavors of quarks without an anomaly. The model also contains a coupling that can be used to break the $\mathrm{U}_A(1)$ symmetry and thus mimic the QCD anomaly. At low temperatures $T$ and small baryon chemical potential $\mu_B$ the model contains massless pions and massive bosonic baryons similar to QCD with an even number of colors. In this work we study the $T-\mu_B$ phase diagram of the model and show that it contains three phases : (1) A chirally broken phase at low $T$ and $\mu_B$, (2) a chirally symmetric baryon superfluid phase at low $T$ and high $\mu_B$, and (3) a symmetric phase at high $T$. We find that the nature of the finite temperature chiral phase transition and in particular the location of the tricritical point that seperates the first order line from the second order line is affected significantly by the anomaly.