Matrix supergroup Chern-Simons models for vortex-antivortex systems

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.

62 pages, 5 figures; v3: published version in JHEP

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Cited by in corpus (5)

• Super instanton counting and localization
• Quantum Integrable Systems from Supergroup Gauge Theories
• ADHM Wilson line defect indices
• Generalized Calogero-Moser system and supergroup gauge origami
• Quantum Algebra of Chern-Simons Matrix Model and Large $N$ Limit