Matrix supergroup Chern-Simons models for vortex-antivortex systems

A bstract We study a U( N | M ) supermatrix Chern-Simons model with an SU( p | q ) internal symmetry. We propose that the model describes a system consisting of N vortices and M antivortices involving SU( p | q ) internal spin degrees of freedom. We present both classical and quantum ground state solutions, and demonstrate the relation to Calogero models. We present evidence that a large N limit describes SU( p | q ) WZW models. In particular, we derive s u ^ p | q Kac-Moody algebras. We also present some results on the calculation of the partition function involving a supersymmetric generalization of the Hall-Littlewood polynomials, indicating the mock modular properties.