Non-Abelian Chern-Simons models with discrete gauge groups on a lattice

Benoît Douçot (1) , L. B. Ioffe

1 LPTHE - Laboratoire de Physique Théorique et Hautes Energies

We construct the local Hamiltonian description of the Chern-Simons theory with discrete non-Abelian gauge group on a lattice. We show that the theory is fully determined by the phase factors associated with gauge transformations and classify all possible non-equivalent phase factors. We also construct the gauge invariant electric field operators that move fluxons around and create/anihilate them. We compute the resulting braiding properties of the fluxons. We apply our general results to the simplest class of non-Abelian groups, dihedral groups D_n.

Domaines: Autre [cond-mat.other]

Benoît Douçot, L. B. Ioffe. Non-Abelian Chern-Simons models with discrete gauge groups on a lattice. New Journal of Physics, 2005, 7, pp.187. ⟨hal-00102593⟩