Three-Dimensional Spin TFTs from Gauging Line Defects
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866911931833516032 |
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| author | Gröne, Jannik Runkel, Ingo |
| author_facet | Gröne, Jannik Runkel, Ingo |
| contents | From the input of an oriented three-dimensional TFT with framed line defects and a commutative $Δ$-separable Frobenius algebra $A$ in the ribbon category of these line defects, we construct a three-dimensional spin TFT. The framed line defects of the spin TFT are labelled by certain equivariant modules over $A$, and the spin structure may or may not extend to a given line defect. Physically the spin TFT can be interpreted as the result of gauging a one-form symmetry in the original oriented TFT. This spin TFT extends earlier constructions in Blanchet-Masbaum (1996) and Blanchet (2005) [arXiv:math/0303240], and it reproduces the classification of abelian spin Chern-Simons theories in Belov-Moore (2005) [arXiv:hep-th/0505235]. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_17336 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Three-Dimensional Spin TFTs from Gauging Line Defects Gröne, Jannik Runkel, Ingo Geometric Topology High Energy Physics - Theory Quantum Algebra From the input of an oriented three-dimensional TFT with framed line defects and a commutative $Δ$-separable Frobenius algebra $A$ in the ribbon category of these line defects, we construct a three-dimensional spin TFT. The framed line defects of the spin TFT are labelled by certain equivariant modules over $A$, and the spin structure may or may not extend to a given line defect. Physically the spin TFT can be interpreted as the result of gauging a one-form symmetry in the original oriented TFT. This spin TFT extends earlier constructions in Blanchet-Masbaum (1996) and Blanchet (2005) [arXiv:math/0303240], and it reproduces the classification of abelian spin Chern-Simons theories in Belov-Moore (2005) [arXiv:hep-th/0505235]. |
| title | Three-Dimensional Spin TFTs from Gauging Line Defects |
| topic | Geometric Topology High Energy Physics - Theory Quantum Algebra |
| url | https://arxiv.org/abs/2406.17336 |