# Vacuum structure of bifundamental gauge theories at finite topological angles

## TL;DR

This paper investigates the vacuum structures of bifundamental $SU(n) imes SU(n)$ gauge theories at finite topological angles, using anomaly constraints and phase diagrams to understand confinement mechanisms.

## Contribution

It provides a detailed analysis of mixed 't Hooft anomalies and proposes phase diagrams consistent with these constraints for bifundamental gauge theories.

## Key findings

- Identifies constraints on vacuum structures from anomaly considerations.
- Proposes phase diagrams compatible with anomaly constraints.
- Offers a heuristic explanation based on dual superconductor confinement.

## Abstract

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.