  We discuss possible vacuum structures of $SU(n)\times SU(n)$ gauge theories
with bifundamental matters at finite $\theta$ angles. In order to give a
precise constraint, a mixed 't Hooft anomaly is studied in detail by gauging
the center $\mathbb{Z}_n$ one-form symmetry of the bifundamental gauge theory.
We propose phase diagrams that are consistent with the constraints, and also
give a heuristic explanation of the result based on the dual superconductor
scenario of confinement.
