Yui Hayashi
(YITP, Kyoto University)
We study non-invertible defects constructed from dualities in the Cardy-Rabinovici model. The Cardy-Rabinovici model is a four-dimensional lattice gauge theory with both electrically and magnetically charged particles, which is used as a playground for investigating the dynamics of the Yang-Mills theory with angle. A notable feature of this model is that the conjectured phase diagram has the electromagnetic invariance generated by and transformations. Although this model does not enjoy the duality in a naive way, we notice that the transformations can be understood as dualities between the Cardy-Rabinovici model and 1-form gauged one. Based on this observation, we construct non-invertible symmetries and determine their non-group-like fusion rules in a formal continuum description of the Cardy-Rabinovici model. Moreover, for some self-dual points, we find that this symmetry turns out to have a mixed gravitational anomaly, which rules out the trivially gapped phase. We also address how the conjectured phase diagram matches this anomaly. This talk is based on arXiv:2204.07440 [hep-th].
Yui Hayashi
(YITP, Kyoto University)
Yuya Tanizaki
(YITP, Kyoto University)