Matrix supergroup Chern-Simons models for vortex-antivortex systems

TL;DR

This paper introduces a supermatrix Chern-Simons model for vortex-antivortex systems with internal symmetries, connecting it to Calogero and WZW models, and exploring its algebraic and partition function properties.

Contribution

It proposes a novel supermatrix Chern-Simons framework for vortex-antivortex systems with internal symmetries, linking classical and quantum solutions to advanced algebraic structures.

Findings

Classical and quantum ground states identified.

Connection established to Calogero and WZW models.

Partition function involves supersymmetric Hall-Littlewood polynomials.

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 $\widehat{\mathfrak{su}}(p|q)$ 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.