ABSTRACT
We study a U(N) gauged matrix quantum mechanics which, in the large N limit, is closely related to the chiral WZW conformal field theory. This manifests itself in two ways. First, we construct the left-moving Kac-Moody algebra from matrix degrees of freedom. Secondly, we compute the partition function of the matrix model in terms of Schur and Kostka polynomials and show that, in the large N limit, it coincides with the partition function of the WZW model. This same matrix model was recently shown to describe non-Abelian quantum Hall states and the relationship to the WZW model can be understood in this framework.
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Dorey, N., Tong, D. & Turner, C. A matrix model for WZW. J. High Energ. Phys. 2016, 7 (2016). https://doi.org/10.1007/JHEP08(2016)007
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DOI: https://doi.org/10.1007/JHEP08(2016)007