# The 39th International Symposium on Lattice Field Theory (Lattice 2022)

Aug 8 – 13, 2022
Hörsaalzentrum Poppelsdorf
Europe/Berlin timezone

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

Aug 9, 2022, 4:50 PM
20m
CP1-HSZ/1st-1.001 - HS5 (CP1-HSZ)

### CP1-HSZ/1st-1.001 - HS5

#### CP1-HSZ

50
Oral Presentation Vacuum Structure, Confinement, and Chiral Symmetry

### Speaker

Yui Hayashi (YITP, Kyoto University)

### Description

We study non-invertible defects constructed from dualities in the Cardy-Rabinovici model. The Cardy-Rabinovici model is a four-dimensional $U(1)$ 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 $\theta$ angle. A notable feature of this model is that the conjectured phase diagram has the electromagnetic $SL(2, \mathbb{Z})$ invariance generated by $S$ and $T$ transformations. Although this model does not enjoy the $SL(2, \mathbb{Z})$ duality in a naive way, we notice that the $SL(2, \mathbb{Z})$ transformations can be understood as dualities between the Cardy-Rabinovici model and $\mathbb{Z}_N$ 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].

### Primary authors

Yui Hayashi (YITP, Kyoto University) Yuya Tanizaki (YITP, Kyoto University)