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

TL;DR

This work demonstrates that a mixed 't Hooft anomaly involving center-related and axial symmetries persists in massless N-flavor QCD under a $Z_N$ flavor-twisted boundary condition, even at finite temperature and chemical potential. By computing the anomaly with two-form background fields and its reduction under circle compactification, the authors show that a trivial, symmetric, gapped phase is forbidden across the finite-(T,μ) plane. They analyze calculable limits, finding that high-T dynamics reproduce center-symmetry breaking while high-μ dynamics favor color-superconducting phases, with CFL/2SC/uSC patterns that respect anomaly matching. The results provide a nonperturbative constraint on the phase diagram, consistent with lattice findings in known regimes and offering predictions for strongly coupled, sign-problem regions where conventional methods fail.

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-$(T,μ)$ phase diagram in QCD-type theories based on anomaly matching related to center and discrete axial symmetries.

Figures (1)

• Figure 1: Two examples of schematic $(T,\mu)$ phase diagrams of massless $\mathbb{Z}_N$-QCD ($N=3$) that are consistent with anomaly. Dashed lines show the phase transition lines, and corresponding symmetry breaking pattern in each phase is specified. $T_{\mathrm{chiral}}$ and $T_{\mathrm{deconf}}$ denote the chiral restoration and deconfinement temperatures, respectively.