Matrix supergroup Chern-Simons models for vortex-antivortex systems

We study a $U(N\mathrm{\mid }M)$ supermatrix Chern-Simons model with an $SU(p\mathrm{\mid }q)$ internal symmetry. We propose that the model describes a system consisting of $N$ vortices and $M$ antivortices involving $SU(p\mathrm{\mid }q)$ 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 $SU(p\mathrm{\mid }q)$ WZW models. In particular, we derive $\widehat{\mathfrak{s}\mathfrak{u}}(p\mathrm{\mid }q)$ 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.