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Matrix supergroup Chern-Simons models for vortex-antivortex systems

Okazaki, Tadashi; Smith, Douglas J.

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Tadashi Okazaki


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.


Okazaki, T., & Smith, D. J. (2018). Matrix supergroup Chern-Simons models for vortex-antivortex systems. Journal of High Energy Physics, 2018(2), Article 118.

Journal Article Type Article
Acceptance Date Feb 13, 2018
Online Publication Date Feb 20, 2018
Publication Date Feb 20, 2018
Deposit Date Feb 28, 2018
Publicly Available Date Mar 2, 2018
Journal Journal of High Energy Physics
Print ISSN 1126-6708
Publisher Scuola Internazionale Superiore di Studi Avanzati (SISSA)
Peer Reviewed Peer Reviewed
Volume 2018
Issue 2
Article Number 118


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Copyright 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.

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