Coset Constructions in Chern-Simons Gauge Theory

Abstract

Coset constructions in the framework of Chern-Simons topological gauge theories are studied. Two examples are considered: models of the types ${U(1)_p\times U(1)_q\over U(1)_{p+q}}\cong U(1)_{pq(p+q)}$ with $p$ and $q$ coprime integers, and ${SU(2)_m\times SU(2)_1\over SU(2)_{m+1}}$. In the latter case it is shown that the Chern-Simons wave functionals can be identified with t he characters of the minimal unitary models, and an explicit representation of the knot (Verlinde) operators acting on the space of $c<1$ characters is obtained.