Matrix supergroup Chern-Simons models for vortex-antivortex systems

Abstract

Abstract 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 su^p|q $$ \widehat{\mathfrak{su}}\left(p\Big|q\right) $$ 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.

Keywords

• Chern-Simons Theories
• Field Theories in Lower Dimensions
• Matrix Models
• Solitons Monopoles and Instantons