Diagrammatic state sums for 2D pin-minus TQFTs
Abstract The two dimensional state sum models of Barrett and Tavares are extended to unoriented spacetimes. The input to the construction is an algebraic structure dubbed half twist algebras, a class of examples of which is real separable superalgebras with a continuous parameter. The construction g...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2020-03-01
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| Series: | Journal of High Energy Physics |
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| Online Access: | http://link.springer.com/article/10.1007/JHEP03(2020)019 |
| _version_ | 1819241719535763456 |
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| author | Alex Turzillo |
| author_facet | Alex Turzillo |
| author_sort | Alex Turzillo |
| collection | DOAJ |
| description | Abstract The two dimensional state sum models of Barrett and Tavares are extended to unoriented spacetimes. The input to the construction is an algebraic structure dubbed half twist algebras, a class of examples of which is real separable superalgebras with a continuous parameter. The construction generates pin-minus TQFTs, including the root invertible theory with partition function the Arf-Brown-Kervaire invariant. Decomposability, the stacking law, and Morita invariance of the construction are discussed. |
| first_indexed | 2024-12-23T14:28:23Z |
| format | Article |
| id | doaj.art-240b6e92effc42b1baca823e3d091b3a |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-12-23T14:28:23Z |
| publishDate | 2020-03-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-240b6e92effc42b1baca823e3d091b3a2022-12-21T17:43:35ZengSpringerOpenJournal of High Energy Physics1029-84792020-03-012020312710.1007/JHEP03(2020)019Diagrammatic state sums for 2D pin-minus TQFTsAlex Turzillo0California Institute of TechnologyAbstract The two dimensional state sum models of Barrett and Tavares are extended to unoriented spacetimes. The input to the construction is an algebraic structure dubbed half twist algebras, a class of examples of which is real separable superalgebras with a continuous parameter. The construction generates pin-minus TQFTs, including the root invertible theory with partition function the Arf-Brown-Kervaire invariant. Decomposability, the stacking law, and Morita invariance of the construction are discussed.http://link.springer.com/article/10.1007/JHEP03(2020)019Topological Field TheoriesLattice Quantum Field TheoryTopological States of Matter |
| spellingShingle | Alex Turzillo Diagrammatic state sums for 2D pin-minus TQFTs Journal of High Energy Physics Topological Field Theories Lattice Quantum Field Theory Topological States of Matter |
| title | Diagrammatic state sums for 2D pin-minus TQFTs |
| title_full | Diagrammatic state sums for 2D pin-minus TQFTs |
| title_fullStr | Diagrammatic state sums for 2D pin-minus TQFTs |
| title_full_unstemmed | Diagrammatic state sums for 2D pin-minus TQFTs |
| title_short | Diagrammatic state sums for 2D pin-minus TQFTs |
| title_sort | diagrammatic state sums for 2d pin minus tqfts |
| topic | Topological Field Theories Lattice Quantum Field Theory Topological States of Matter |
| url | http://link.springer.com/article/10.1007/JHEP03(2020)019 |
| work_keys_str_mv | AT alexturzillo diagrammaticstatesumsfor2dpinminustqfts |