Symmetry TFT for Subsystem Symmetry
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866914745449185280 |
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| author | Cao, Weiguang Jia, Qiang |
| author_facet | Cao, Weiguang Jia, Qiang |
| contents | We generalize the idea of symmetry topological field theory (SymTFT) for subsystem symmetry. We propose the 2-foliated BF theory with level $N$ in $(3+1)$d as subsystem SymTFT for subsystem $\mathbb Z_N$ symmetry in $(2+1)$d. Focusing on $N=2$, we investigate various topological boundaries. The subsystem Kramers-Wannier and Jordan-Wigner dualities can be viewed as boundary transformations of the subsystem SymTFT and are included in a larger duality web from the subsystem $SL(2,\mathbb Z_2)$ symmetry of the bulk foliated BF theory. Finally, we construct the condensation defects and twist defects of $S$-transformation in the subsystem $SL(2,\mathbb Z_2)$, from which the fusion rule of subsystem non-invertible operators can be recovered. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2310_01474 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Symmetry TFT for Subsystem Symmetry Cao, Weiguang Jia, Qiang High Energy Physics - Theory Strongly Correlated Electrons We generalize the idea of symmetry topological field theory (SymTFT) for subsystem symmetry. We propose the 2-foliated BF theory with level $N$ in $(3+1)$d as subsystem SymTFT for subsystem $\mathbb Z_N$ symmetry in $(2+1)$d. Focusing on $N=2$, we investigate various topological boundaries. The subsystem Kramers-Wannier and Jordan-Wigner dualities can be viewed as boundary transformations of the subsystem SymTFT and are included in a larger duality web from the subsystem $SL(2,\mathbb Z_2)$ symmetry of the bulk foliated BF theory. Finally, we construct the condensation defects and twist defects of $S$-transformation in the subsystem $SL(2,\mathbb Z_2)$, from which the fusion rule of subsystem non-invertible operators can be recovered. |
| title | Symmetry TFT for Subsystem Symmetry |
| topic | High Energy Physics - Theory Strongly Correlated Electrons |
| url | https://arxiv.org/abs/2310.01474 |