Anyons in discrete gauge theories with Chern-Simons terms

Details Anyons in discrete gauge theories with Chern-Simons terms Anyons in discrete gauge theories with Chern-Simons terms

1992-03-17

arxiv.org/abs/hep-th/9203047v1

Nucl.Phys. B393 (1993) 547-570

Physics

High Energy Physics

High Energy Physics - Theory

18 pages

Scientific paper

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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