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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 aconsequence, massless $\mathbb{Z}_N$-QCD turns out to realize persistent orderat any temperatures and quark chemical potentials, namely, the symmetric andgapped phase is strictly forbidden. This is the first result on thefinite-$(T,\mu)$ phase diagram in QCD-type theories based on anomaly matchingrelated to center and discrete axial symmetries.

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