Non-invertible self-duality defects of Cardy-Rabinovici model and mixed gravitational anomaly

Yukawa Institute for Theoretical Physics, Kyoto University, Kitashirakawa Oiwakecho, Sakyo Ward, Kyoto, 606-8502, Japan.

^* e-mail: yui.hayashi@yukawa.kyoto-u.ac.jp
^** e-mail: yuya.tanizaki@yukawa.kyoto-u.ac.jp

Published online: 22 December 2022

Abstract

We study new symmetries of the Cardy-Rabinovici model and their dynamical applications. The Cardy-Rabinovici model is a 4d U(1) gauge theory with electric and magnetic matters, which is a good playground for studying the dynamics of the Yang-Mills theory with θ angle. In this model, the electromagnetic S L(2, ℤ) self-duality is not realized in a naive way. Still, the S L(2, ℤ) transformations become legitimate duality operations by appropriately gauging the ℤ_N 1-form symmetry. We construct new noninvertible symmetries from this duality at self-dual points and determine their non-group-like fusion rules. As an application, we can rule out the trivially gapped phase for some self-dual parameters due to a mixed gravitational anomaly of this new symmetry. We also show how the conjectured phase diagram of the Cardy-Rabinovici model is consistent with this anomaly matching condition.