Topological aspects of $4$D Abelian lattice gauge theories with the $\theta$ parameter

Understand

We study a four-dimensional $U(1)$ gauge theory with the $\theta$ angle, which was originally proposed by Cardy and Rabinovici.

• It is known that the model has the rich phase diagram thanks to the presence of both electrically and magnetically charged particles.
• We discuss the topological nature of the oblique confinement phase of the model at $\theta=\pi$, and show how its appearance can be consistent with the anomaly constraint.
• We also construct the $SL(2,\mathbb{Z})$ self-dual theory out of the Cardy-Rabinovici model by gauging a part of its one-form symmetry.