Two-dimensional state sum models and spin structures

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

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.

Citation

Barrett, J. W., & Tavares, S. O. G. (2014). Two-dimensional state sum models and spin structures. Communications in Mathematical Physics, 336(1), 63-100. doi:10.1007/s00220-014-2246-z

• 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