Chern-Simons theory and the quantum Racah formula

TL;DR

This paper extends Chern-Simons theory results to general groups and link colorings, providing a non-perturbative evaluation of Wilson loop observables and deriving the quantum Racah formula heuristically.

Contribution

It generalizes previous Chern-Simons results to broader settings and offers a new heuristic derivation of the quantum Racah formula.

Findings

Wilson loop observables match Turaev's shadow invariant

Non-perturbative evaluation achieved for certain links

Heuristic path integral derivation of the quantum Racah formula

Abstract

We generalize several results on Chern-Simons models on Sigma x S1 in the so-called "torus gauge" which were obtained in arXiv:math-ph/0507040 to the case of general (simply-connected simple compact) structure groups and general link colorings. In particular, we give a non-perturbative evaluation of the Wilson loop observables corresponding to a special class of simple but non-trivial links and show that their values are given by Turaev's shadow invariant. As a byproduct we obtain a heuristic path integral derivation of the quantum Racah formula.