https://doi.org/10.1051/epjconf/202227402010
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
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 ℤN 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.
© The Authors, published by EDP Sciences, 2022
This is an Open Access article distributed under the terms of the Creative Commons Attribution License 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
