  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.
