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arXiv · 2405.13105

Non-invertible and higher-form symmetries in 2+1d lattice gauge theories

Yichul Choi·Yaman Sanghavi·Shu-Heng Shao·Yunqin Zheng
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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.

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Yichul Choi, Yaman Sanghavi, Shu-Heng Shao, Yunqin Zheng. 2024-05-21. Non-invertible and higher-form symmetries in 2+1d lattice gauge theories. https://doi.org/10.21468/scipostphys.18.1.008

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