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Duality and self-duality in Ginzburg-Landau theory with Chern-Simons term

Hagen Kleinert·Flavio S. Nogueira
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Abstract

We derive the exact dual theory of a lattice Ginzburg-Landau theory with an additional topological Chern-Simons (CS) term. It is shown that in the zero-temperature limit, the statistical parameter $θ=1/2π$ corresponds to a fixed point of the duality transformation. Thus we have found a nontrivial example of self-duality in three dimensions. In this scenario, the specialization of anyonic to fermionic statistics my be viewed as a phase transition.

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Hagen Kleinert, Flavio S. Nogueira. 2001-10-25. Duality and self-duality in Ginzburg-Landau theory with Chern-Simons term. https://arxiv.org/abs/cond-mat/0110513

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