Non-invertible and higher-form symmetries in 2+1d lattice gauge theories
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...
Saved in:
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
SciPost
2025-01-01
|
| Series: | SciPost Physics |
| Online Access: | https://scipost.org/SciPostPhys.18.1.008 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1841553286050611200 |
|---|---|
| author | Yichul Choi, Yaman Sanghavi, Shu-Heng Shao, Yunqin Zheng |
| author_facet | Yichul Choi, Yaman Sanghavi, Shu-Heng Shao, Yunqin Zheng |
| author_sort | Yichul Choi, Yaman Sanghavi, Shu-Heng Shao, Yunqin Zheng |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-6b0e05a259b442c7a33a0c2c1d12b101 |
| institution | Kabale University |
| issn | 2542-4653 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | SciPost |
| record_format | Article |
| series | SciPost Physics |
| spelling | doaj-art-6b0e05a259b442c7a33a0c2c1d12b1012025-01-09T11:22:34ZengSciPostSciPost Physics2542-46532025-01-0118100810.21468/SciPostPhys.18.1.008Non-invertible and higher-form symmetries in 2+1d lattice gauge theoriesYichul Choi, Yaman Sanghavi, Shu-Heng Shao, Yunqin ZhengWe 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.https://scipost.org/SciPostPhys.18.1.008 |
| spellingShingle | Yichul Choi, Yaman Sanghavi, Shu-Heng Shao, Yunqin Zheng Non-invertible and higher-form symmetries in 2+1d lattice gauge theories SciPost Physics |
| title | Non-invertible and higher-form symmetries in 2+1d lattice gauge theories |
| title_full | Non-invertible and higher-form symmetries in 2+1d lattice gauge theories |
| title_fullStr | Non-invertible and higher-form symmetries in 2+1d lattice gauge theories |
| title_full_unstemmed | Non-invertible and higher-form symmetries in 2+1d lattice gauge theories |
| title_short | Non-invertible and higher-form symmetries in 2+1d lattice gauge theories |
| title_sort | non invertible and higher form symmetries in 2 1d lattice gauge theories |
| url | https://scipost.org/SciPostPhys.18.1.008 |
| work_keys_str_mv | AT yichulchoiyamansanghavishuhengshaoyunqinzheng noninvertibleandhigherformsymmetriesin21dlatticegaugetheories |