Anyons and gaussian conformal field theories

Abstract

We identify the spin of the anyons with the holomorphic dimension of the primary fields of a Gaussian conformal field theory. The angular momentum addition rules for anyons go over to the fusion rules for the primary fields and the r ↔ 1/2r duality of the Gaussian CFT is reproduced by a charge-flux duality of the anyons. For a U(1) Chern-Simons theory with topological mass parameter k = 2n, N-anyon states on the torus have 2n components, which correspond to the 2n conformal blocks of an N-point function in the Gaussian conformal field theory.