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}}left(pBig|qright) 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.
Highlights
Matrix Chern-Simons models [1, 2] are gauged quantum mechanics models whose Lagrangian is first order in time derivatives
Susskind [3] proposed that the infinite-dimensional matrix Chern-Simons quantum mechanical model, as the non-commutative Chern-Simons theory on a plane, could describe the Laughlin theory [4] in such a way that the positions of an infinite number of electrons moving in a two-dimensional plane influenced under strong magnetic field correspond to infinite matrices
We have studied a (0 + 1)-dimensional U(N |M ) matrix Chern-Simons quantum mechanics with an SU(p|q) global symmetry
Summary
Matrix Chern-Simons models [1, 2] are gauged quantum mechanics models whose Lagrangian is first order in time derivatives. It has been argued that this extended model describes the non-Abelian quantum Hall effect with internal spin degrees of freedom Another remarkable application of the U(N ) matrix Chern-Simons model has been proposed by Tong [12]. A further generalization has been argued in [2] that the U(N ) matrix ChernSimons model with an SU(p) global symmetry is the effective description of N vortices in non-relativistic U(p) Chern-Simons matter theories.
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