Dichromatic state sum models for four-manifolds from pivotal functors
A family of invariants of smooth, oriented four-dimensional manifolds is defined via handle decompositions and the Kirby calculus of framed link diagrams. The invariants are parametrised by a pivotal functor from a spherical fusion category into a ribbon fusion category. A state sum formula for the...
| Main Authors: | , |
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| Format: | Article |
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Springer
2018
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| Online Access: | https://eprints.nottingham.ac.uk/47124/ |
| _version_ | 1848797472221036544 |
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| author | Bärenz, Manuel Barrett, John W. |
| author_facet | Bärenz, Manuel Barrett, John W. |
| author_sort | Bärenz, Manuel |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | A family of invariants of smooth, oriented four-dimensional manifolds is defined via handle decompositions and the Kirby calculus of framed link diagrams. The invariants are parametrised by a pivotal functor from a spherical fusion category into a ribbon fusion category.
A state sum formula for the invariant is constructed via the chain-mail procedure, so a large class of topological state sum models can be expressed as link invariants. Most prominently, the Crane-Yetter state sum over an arbitrary ribbon fusion category is recovered, including the nonmodular case. It is shown that the Crane-Yetter invariant for nonmodular categories is stronger than signature and Euler invariant.
A special case is the four-dimensional untwisted Dijkgraaf-Witten model. Derivations of state space dimensions of TQFTs arising from the state sum model agree with recent calculations of ground state degeneracies in Walker-Wang models.
Relations to different approaches to quantum gravity such as Cartan geometry and teleparallel gravity are also discussed. |
| first_indexed | 2025-11-14T20:04:25Z |
| format | Article |
| id | nottingham-47124 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| last_indexed | 2025-11-14T20:04:25Z |
| publishDate | 2018 |
| publisher | Springer |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-471242020-05-04T19:43:47Z https://eprints.nottingham.ac.uk/47124/ Dichromatic state sum models for four-manifolds from pivotal functors Bärenz, Manuel Barrett, John W. A family of invariants of smooth, oriented four-dimensional manifolds is defined via handle decompositions and the Kirby calculus of framed link diagrams. The invariants are parametrised by a pivotal functor from a spherical fusion category into a ribbon fusion category. A state sum formula for the invariant is constructed via the chain-mail procedure, so a large class of topological state sum models can be expressed as link invariants. Most prominently, the Crane-Yetter state sum over an arbitrary ribbon fusion category is recovered, including the nonmodular case. It is shown that the Crane-Yetter invariant for nonmodular categories is stronger than signature and Euler invariant. A special case is the four-dimensional untwisted Dijkgraaf-Witten model. Derivations of state space dimensions of TQFTs arising from the state sum model agree with recent calculations of ground state degeneracies in Walker-Wang models. Relations to different approaches to quantum gravity such as Cartan geometry and teleparallel gravity are also discussed. Springer 2018-06-30 Article PeerReviewed Bärenz, Manuel and Barrett, John W. (2018) Dichromatic state sum models for four-manifolds from pivotal functors. Communications in Mathematical Physics, 360 (2). pp. 663-714. ISSN 1432-0916 https://link.springer.com/article/10.1007%2Fs00220-017-3012-9 doi:10.1007/s00220-017-3012-9 doi:10.1007/s00220-017-3012-9 |
| spellingShingle | Bärenz, Manuel Barrett, John W. Dichromatic state sum models for four-manifolds from pivotal functors |
| title | Dichromatic state sum models for four-manifolds from pivotal functors |
| title_full | Dichromatic state sum models for four-manifolds from pivotal functors |
| title_fullStr | Dichromatic state sum models for four-manifolds from pivotal functors |
| title_full_unstemmed | Dichromatic state sum models for four-manifolds from pivotal functors |
| title_short | Dichromatic state sum models for four-manifolds from pivotal functors |
| title_sort | dichromatic state sum models for four-manifolds from pivotal functors |
| url | https://eprints.nottingham.ac.uk/47124/ https://eprints.nottingham.ac.uk/47124/ https://eprints.nottingham.ac.uk/47124/ |