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Two-dimensional state sum models and spin structures

Barrett, John W.; Tavares, Sara O. G.

Authors

JOHN BARRETT john.barrett@nottingham.ac.uk
Professor of Mathematical Physics

Sara O. G. Tavares



Abstract

The state sum models in two dimensions introduced by Fukuma, Hosono and Kawai are generalised by allowing algebraic data from a non-symmetric Frobenius algebra. Without any further data, this leads to a state sum model on the sphere. When the data is augmented with a crossing map, the partition function is defined for any oriented surface with a spin structure. An algebraic condition that is necessary for the state sum model to be sensitive to spin structure is determined. Some examples of state sum models that distinguish topologically-inequivalent spin structures are calculated.

Journal Article Type Article
Acceptance Date Jul 14, 2014
Publication Date Dec 25, 2014
Deposit Date Nov 2, 2017
Print ISSN 0010-3616
Electronic ISSN 1432-0916
Publisher BMC
Peer Reviewed Peer Reviewed
Volume 336
Issue 1
Pages 63-100
DOI https://doi.org/10.1007/s00220-014-2246-z
Public URL http://link.springer.com/article/10.1007/s00220-014-2246-z
Publisher URL https://link.springer.com/article/10.1007%2Fs00220-014-2246-z