Anomaly matching for the phase diagram of massless ZN-QCD

We elucidate that the phase diagram of massless N-flavor QCD under a Z(N) flavor-twisted boundary condition (massless Z(N)-QCD) is constrained by a 't Hooft anomaly involving two-form gauge fields. As a consequence, massless Z(N)-QCD turns out to realize persistent order at any temperature and quark chemical potential; 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.