Dichromatic state sum models for four-manifolds from pivotal functors

Bärenz, Manuel and Barrett, John W. (2017) Dichromatic state sum models for four-manifolds from pivotal functors. Communications in Mathematical Physics . ISSN 1432-0916

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Abstract

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.

Item Type: Article
Schools/Departments: University of Nottingham, UK > Faculty of Science > School of Mathematical Sciences
Identification Number: 10.1007/s00220-017-3012-9
Depositing User: Eprints, Support
Date Deposited: 12 Oct 2017 07:46
Last Modified: 13 Dec 2017 05:34
URI: http://eprints.nottingham.ac.uk/id/eprint/47124

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