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Anyons in discrete gauge theories with Chern-Simons terms

F. Alexander Bais·Peter van Driel·Mark de Wild Propitius
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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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F. Alexander Bais, Peter van Driel, Mark de Wild Propitius. 1992-03-17. Anyons in discrete gauge theories with Chern-Simons terms. https://doi.org/10.1016/0550-3213(93)90073-x

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