Matrix supergroup Chern-Simons models for vortex-antivortex systems

Okazaki, Tadashi; Smith, Douglas J.

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 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.

Citation

Okazaki, T., & Smith, D. J. (2018). Matrix supergroup Chern-Simons models for vortex-antivortex systems. Journal of High Energy Physics, 2018(2), Article 118. https://doi.org/10.1007/jhep02%282018%29119

• 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
• Electronic ISSN: 1029-8479
• Publisher: Scuola Internazionale Superiore di Studi Avanzati (SISSA)
• Peer Reviewed: Peer Reviewed
• Volume: 2018
• Issue: 2
• Article Number: 118
• DOI: https://doi.org/10.1007/jhep02%282018%29119
• Public URL: https://durham-repository.worktribe.com/output/1338738