A Matrix Model for WZW

TL;DR

This paper demonstrates that a U(N) gauged matrix quantum mechanics model reproduces the chiral WZW conformal field theory in the large N limit, linking matrix degrees of freedom to Kac-Moody algebra and partition functions.

Contribution

It constructs the left-moving Kac-Moody algebra from matrix variables and shows the matrix model's partition function matches the WZW model's in the large N limit.

Findings

Constructed the Kac-Moody algebra from matrix degrees of freedom.

Computed the partition function using Schur and Kostka polynomials.

Established the equivalence of the matrix model and WZW partition functions in the large N limit.

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.