Non-invertible and higher-form symmetries in 2+1d lattice gauge theories
Yichul Choi, Yaman Sanghavi, Shu-Heng Shao, Yunqin Zheng
SciPost Phys. 18, 008 (2025) · published 9 January 2025
- doi: 10.21468/SciPostPhys.18.1.008
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Abstract
We explore exact generalized symmetries in the standard 2+1d lattice $\mathbb{Z}_2$ gauge theory coupled to the Ising model, and compare them with their continuum field theory counterparts. One model has a (non-anomalous) non-invertible symmetry, and we identify two distinct non-invertible symmetry protected topological phases. The non-invertible algebra involves a lattice condensation operator, which creates a toric code ground state from a product state. Another model has a mixed anomaly between a 1-form symmetry and an ordinary symmetry. This anomaly enforces a nontrivial transition in the phase diagram, consistent with the "Higgs=SPT" proposal. Finally, we discuss how the symmetries and anomalies in these two models are related by gauging, which is a 2+1d version of the Kennedy-Tasaki transformation.
Cited by 7
Authors / Affiliations: mappings to Contributors and Organizations
See all Organizations.- 1 2 Yichul Choi,
- 1 Yaman Sanghavi,
- 1 Shu-Heng Shao,
- 1 Yunqin Zheng