Dichromatic state sum models for four-manifolds from pivotal functors
Bärenz, Manuel; Barrett, John W.
JOHN BARRETT email@example.com
Professor of Mathematical Physics
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.
Bärenz, M., & Barrett, J. W. (2018). Dichromatic state sum models for four-manifolds from pivotal functors. Communications in Mathematical Physics, 360(2), https://doi.org/10.1007/s00220-017-3012-9
|Journal Article Type||Article|
|Acceptance Date||Aug 27, 2017|
|Online Publication Date||Nov 24, 2017|
|Publication Date||Jun 30, 2018|
|Deposit Date||Oct 12, 2017|
|Publicly Available Date||Nov 24, 2017|
|Journal||Communications in Mathematical Physics|
|Peer Reviewed||Peer Reviewed|
|Copyright Statement||Copyright information regarding this work can be found at the following address: http://creativecommons.org/licenses/by/4.0|
Copyright information regarding this work can be found at the following address: http://creativecommons.org/licenses/by/4.0
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