Level-rank duality in Chern-Simons theory

Abstract

We begin investigations of the level-rank duality of pure Chern-Simons theory on the torus by counting the number of states on both sides of the duality. We analyse a formula given in \cite{Elitzur:1989nr} for determining the dimensionality of the Hilbert space of $SU(N)$ Chern-Simons theory on the torus. We illustrate a way to find the dimensions of the $U(N)$ theory and show that it matches with the answer expected from duality.