Finite-Density Massless Two-Color QCD at Isospin Roberge-Weiss Point and 't Hooft Anomaly

TL;DR

This paper investigates the phase structure of massless two-flavor two-color QCD at the isospin Roberge-Weiss point, revealing a 't Hooft anomaly that constrains phase transitions and draws parallels with quantum antiferromagnets.

Contribution

It identifies a novel 't Hooft anomaly involving center, baryon, and isospin symmetries at the RW point, providing new constraints on the phase diagram of QC$_2$D.

Findings

Discovery of a $Z_2$ 't Hooft anomaly at the RW point.

Anomaly matching constrains the phase diagram across all temperatures and chemical potentials.

Comparison with lattice results and effective theories supports the anomaly's implications.

Abstract

We study the phase diagram of two-flavor massless two-color QCD (QC$_2$D) under the presence of quark chemical potentials and imaginary isospin chemical potentials. At the special point of the imaginary isospin chemical potential, called the isospin Roberge--Weiss (RW) point, two-flavor QC$_2$D enjoys the $\mathbb{Z}_2$ center symmetry that acts on both quark flavors and the Polyakov loop. We find a $\mathbb{Z}_2$ 't Hooft anomaly of this system, which involves the $\mathbb{Z}_2$ center symmetry, the baryon-number symmetry, and the isospin chiral symmetry. Anomaly matching, therefore, constrains the possible phase diagram at any temperatures and quark chemical potentials at the isospin RW point, and we compare it with previous results obtained by chiral effective field theory and lattice simulations. We also point out an interesting similarity of two-flavor massless QC$_2$D with $(2+1)$d quantum anti-ferromagnetic systems.