Vanishing of the $H^3$ obstruction for time-reversal symmetry in (2+1)D abelian bosonic TQFTs
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866911383468113920 |
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| author | Orii, Ippo |
| author_facet | Orii, Ippo |
| contents | In $(2+1)$-dimensional topological quantum field theories (TQFTs), the action of a global symmetry group on the anyon system is one of the central topics of research. Owing to the subtle categorical nature of anyons, a global symmetry acting on them is generally realized in a projective manner. Symmetry fractionalization encodes this projective realization. The obstruction to defining symmetry fractionalization is captured by a cohomology class, known as the $H^3$ obstruction, whose nontriviality signals a failure to define symmetry fractionalization consistently. In this short note, we prove that the $H^3$ obstruction for time-reversal symmetry always vanishes in abelian bosonic TQFTs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_07368 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Vanishing of the $H^3$ obstruction for time-reversal symmetry in (2+1)D abelian bosonic TQFTs Orii, Ippo High Energy Physics - Theory Strongly Correlated Electrons Mathematical Physics In $(2+1)$-dimensional topological quantum field theories (TQFTs), the action of a global symmetry group on the anyon system is one of the central topics of research. Owing to the subtle categorical nature of anyons, a global symmetry acting on them is generally realized in a projective manner. Symmetry fractionalization encodes this projective realization. The obstruction to defining symmetry fractionalization is captured by a cohomology class, known as the $H^3$ obstruction, whose nontriviality signals a failure to define symmetry fractionalization consistently. In this short note, we prove that the $H^3$ obstruction for time-reversal symmetry always vanishes in abelian bosonic TQFTs. |
| title | Vanishing of the $H^3$ obstruction for time-reversal symmetry in (2+1)D abelian bosonic TQFTs |
| topic | High Energy Physics - Theory Strongly Correlated Electrons Mathematical Physics |
| url | https://arxiv.org/abs/2509.07368 |