Matrix supergroup Chern-Simons models for vortex-antivortex systems

Tadashi Okazaki; Douglas J. Smith

doi:10.1007/jhep02(2018)119

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arXiv · 1712.01370

Matrix supergroup Chern-Simons models for vortex-antivortex systems

Tadashi Okazaki·Douglas J. Smith

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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.

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hep-th cond-mat.mes-hall cond-mat.str-el math-ph math.MP math.RT

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BibTeX RIS

Tadashi Okazaki, Douglas J. Smith. 2017-12-04. Matrix supergroup Chern-Simons models for vortex-antivortex systems. https://doi.org/10.1007/jhep02(2018)119

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