Coset Constructions in Chern-Simons Gauge Theory

TL;DR

This paper explores coset constructions within Chern-Simons gauge theories, demonstrating their relation to minimal models and providing explicit representations of knot operators, advancing understanding of topological quantum field theories.

Contribution

It introduces specific coset models in Chern-Simons theory and connects wave functionals to minimal model characters, offering explicit operator representations.

Findings

Chern-Simons wave functionals correspond to minimal model characters

Explicit knot (Verlinde) operators are constructed

Coset models are explicitly realized in topological gauge theories

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.