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Matrix supergroup Chern-Simons models for vortex-antivortex systems.

Okazaki, Tadashi and Smith, Douglas J. (2018) 'Matrix supergroup Chern-Simons models for vortex-antivortex systems.', Journal of high energy physics., 2018 (2). p. 119.


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 suˆ(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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Publisher statement:This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
Date accepted:13 February 2018
Date deposited:02 March 2018
Date of first online publication:20 February 2018
Date first made open access:02 March 2018

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