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Two-dimensional state sum models and spin structures

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


Professor of Mathematical Physics

Sara O. G. Tavares


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
Public URL
Publisher URL