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 $\frac{U(1{)}_p\times U(1{)}_q}{U(1{)}_{p+q}}\cong U(1{)}_{pq(p+q)}$ with $p$ and $q$ coprime integers, and $\frac{SU(2{)}_m\times SU(2{)}_1}{SU(2{)}_{m+1}}$. 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.

15 pages

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