Foliated BF theories and Multipole symmetries
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866917672549089280 |
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| author | Ebisu, Hiromi Honda, Masazumi Nakanishi, Taiichi |
| author_facet | Ebisu, Hiromi Honda, Masazumi Nakanishi, Taiichi |
| contents | Due to the recent studies of the fracton topological phases, which host deconfined quasi-particle excitations with mobility restrictions, the concept of symmetries have been updated. Focusing on one of such new symmetries, multipole symmetries, including global, dipole, and quadruple symmetries, and gauge fields associated with them, we construct a new sets of $\mathbb{Z}_N$ $2+1d$ foliated BF theories, where BF theories of conventional topological phases are stacked in layers with couplings between them. By investigating gauge invariant non-local operators, we show that our foliated BF theories exhibit unusual ground state degeneracy depending on the system size; it depends on the greatest common divisor between $N$ and the system size. Our result provides a unified insight on UV lattice models of the fracton topological phases and other unconventional ones in view of foliated field theories. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_06701 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Foliated BF theories and Multipole symmetries Ebisu, Hiromi Honda, Masazumi Nakanishi, Taiichi Strongly Correlated Electrons High Energy Physics - Lattice High Energy Physics - Theory Mathematical Physics Quantum Physics Due to the recent studies of the fracton topological phases, which host deconfined quasi-particle excitations with mobility restrictions, the concept of symmetries have been updated. Focusing on one of such new symmetries, multipole symmetries, including global, dipole, and quadruple symmetries, and gauge fields associated with them, we construct a new sets of $\mathbb{Z}_N$ $2+1d$ foliated BF theories, where BF theories of conventional topological phases are stacked in layers with couplings between them. By investigating gauge invariant non-local operators, we show that our foliated BF theories exhibit unusual ground state degeneracy depending on the system size; it depends on the greatest common divisor between $N$ and the system size. Our result provides a unified insight on UV lattice models of the fracton topological phases and other unconventional ones in view of foliated field theories. |
| title | Foliated BF theories and Multipole symmetries |
| topic | Strongly Correlated Electrons High Energy Physics - Lattice High Energy Physics - Theory Mathematical Physics Quantum Physics |
| url | https://arxiv.org/abs/2310.06701 |