Vacuum structure of bifundamental gauge theories at finite topological angles

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.