Anomaly matching for phase diagram of massless $\mathbb{Z}_N$-QCD

TL;DR

This paper uses anomaly matching to analyze the phase diagram of massless $ ext{QCD}$ with $ ext{Z}_N$ flavor-twisted boundary conditions, revealing persistent order and forbidding symmetric gapped phases at all temperatures and chemical potentials.

Contribution

It demonstrates that anomaly constraints prevent the symmetric gapped phase in massless $ ext{Z}_N$-QCD at any temperature or chemical potential.

Findings

Symmetric gapped phase is forbidden at all (T, μ).

Anomaly matching constrains the phase structure of massless $ ext{Z}_N$-QCD.

Persistent order exists across the entire phase diagram.

Abstract

We elucidate that the phase diagram of massless $N$-flavor QCD under $\mathbb{Z}_N$ flavor-twisted boundary condition (massless $\mathbb{Z}_N$-QCD) is constrained by an 't Hooft anomaly involving two-form gauge fields. As a consequence, massless $\mathbb{Z}_N$-QCD turns out to realize persistent order at any temperatures and quark chemical potentials, namely, the symmetric and gapped phase is strictly forbidden. This is the first result on the finite-$(T,\mu)$ phase diagram in QCD-type theories based on anomaly matching related to center and discrete axial symmetries.