Web of dualities on non-orientable surfaces
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
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2026
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| _version_ | 1866917525837578240 |
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| author | Orii, Ippo Tsuji, Keita |
| author_facet | Orii, Ippo Tsuji, Keita |
| contents | It is known that a two-dimensional bosonic theory with a non-anomalous $\mathbb{Z}_2$ symmetry can be fermionized. Recent work shows that if the bosonic theory also has non-anomalous time-reversal symmetry, fermionization extends to non-orientable surfaces and yields a fermionic theory that depends on a $\mathrm{Pin}^-$ structure. Besides fermionization, one can define various topological manipulations, such as gauging and stacking invertible phases, which together generate a web of dualities. We prove that their group structure is the dihedral group $D_8$ of order 16. Furthermore, we systematically investigate the web from two perspectives: Symmetry TFT and actions on sectors of the $S^1$ Hilbert space. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_09067 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Web of dualities on non-orientable surfaces Orii, Ippo Tsuji, Keita High Energy Physics - Theory It is known that a two-dimensional bosonic theory with a non-anomalous $\mathbb{Z}_2$ symmetry can be fermionized. Recent work shows that if the bosonic theory also has non-anomalous time-reversal symmetry, fermionization extends to non-orientable surfaces and yields a fermionic theory that depends on a $\mathrm{Pin}^-$ structure. Besides fermionization, one can define various topological manipulations, such as gauging and stacking invertible phases, which together generate a web of dualities. We prove that their group structure is the dihedral group $D_8$ of order 16. Furthermore, we systematically investigate the web from two perspectives: Symmetry TFT and actions on sectors of the $S^1$ Hilbert space. |
| title | Web of dualities on non-orientable surfaces |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2601.09067 |