Anomaly inflow for dipole symmetry and higher form foliated field theories
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| Format: | Preprint |
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2024
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| _version_ | 1866916391531053056 |
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| author | Ebisu, Hiromi Honda, Masazumi Nakanishi, Taiichi |
| author_facet | Ebisu, Hiromi Honda, Masazumi Nakanishi, Taiichi |
| contents | In accordance with recent progress of fracton topological phases, unusual topological phases of matter hosting fractionalized quasiparticle excitations with mobility constraints, new type of symmetry is studied -- multipole symmetry, associated with conservation of multipoles. Based on algebraic relation between dipole and global charges, we introduce a series of $(d+1)$-dimensional BF theories with $p$-form gauge fields, which admit dipole of spatially extended excitations, and study their physical properties. We elucidate that gauge invariant loops have unusual form, containing linear function of the spatial coordinate, which leads to the position dependent braiding statistics and unusual ground state degeneracy dependence on the system size. We also show that the theories exhibit a mixed 't Hooft anomaly between $p$-form and $(d-p)$-form dipole symmetries, which is canceled by an invertible theory defined in one dimensional higher via anomaly inflow mechanism. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_04919 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Anomaly inflow for dipole symmetry and higher form foliated field theories Ebisu, Hiromi Honda, Masazumi Nakanishi, Taiichi Strongly Correlated Electrons High Energy Physics - Lattice High Energy Physics - Theory Mathematical Physics Quantum Physics In accordance with recent progress of fracton topological phases, unusual topological phases of matter hosting fractionalized quasiparticle excitations with mobility constraints, new type of symmetry is studied -- multipole symmetry, associated with conservation of multipoles. Based on algebraic relation between dipole and global charges, we introduce a series of $(d+1)$-dimensional BF theories with $p$-form gauge fields, which admit dipole of spatially extended excitations, and study their physical properties. We elucidate that gauge invariant loops have unusual form, containing linear function of the spatial coordinate, which leads to the position dependent braiding statistics and unusual ground state degeneracy dependence on the system size. We also show that the theories exhibit a mixed 't Hooft anomaly between $p$-form and $(d-p)$-form dipole symmetries, which is canceled by an invertible theory defined in one dimensional higher via anomaly inflow mechanism. |
| title | Anomaly inflow for dipole symmetry and higher form foliated field theories |
| topic | Strongly Correlated Electrons High Energy Physics - Lattice High Energy Physics - Theory Mathematical Physics Quantum Physics |
| url | https://arxiv.org/abs/2406.04919 |