English

Anyons in discrete gauge theories with Chern-Simons terms

High Energy Physics - Theory 2015-06-26 v1

Abstract

We study the effect of a Chern-Simons term in a theory with discrete gauge group H, which in (2+1)-dimensional space time describes (non-abelian) anyons. As in a previous paper, we emphasize the underlying algebraic structure, namely the Hopf algebra D(H). We argue on physical grounds that the addition of a Chern-Simons term in the action leads to a non-trivial 3-cocycle on D(H). Accordingly, the physically inequivalent models are labelled by the elements of the cohomology group H^3(H,U(1)). It depends periodically on the coefficient of the Chern-Simons term which model is realized. This establishes a relation with the discrete topological field theories of Dijkgraaf and Witten. Some representative examples are worked out explicitly.

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Cite

@article{arxiv.hep-th/9203047,
  title  = {Anyons in discrete gauge theories with Chern-Simons terms},
  author = {F. Alexander Bais and Peter van Driel and Mark de Wild Propitius},
  journal= {arXiv preprint arXiv:hep-th/9203047},
  year   = {2015}
}

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18 pages