We elucidate that the phase diagram of massless N-flavor QCD under a ZN flavor-twisted boundary condition (massless ZN-QCD) is constrained by a 't Hooft anomaly involving two-form gauge fields. As a consequence, massless ZN-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,μ) phase diagram in QCD-type theories based on anomaly matching related to center and discrete axial symmetries.