Description
Non-invertible symmetries of Cardy-Rabinovici model and mixed gravitational anomaly
Abstract:
In this talk, we discuss noninvertible symmetries of the Cardy-Rabinovici model. The Cardy-Rabinovici model is the 4d U(1) gauge theory with electric and magnetic matters. We find that the $SL(2,\mathbb{Z})$ electromagnetic transformations can be understood as dualities between the Cardy-Rabinovici model and its appropriately $\mathbb{Z}_N$ 1-form gauged model. Based on this observation, we can construct noninvertible symmetry defects with non-group-like fusion rules at self-dual parameters. As an application, we show that the mixed gravitational anomaly of this symmetry rules out the trivially gapped vacuum for some parameters. We also reveal how the conjectured phase diagram of the Cardy-Rabinovici model is consistent with this anomaly.
