CHERN–SIMONS THEORY AND THE QUANTUM RACAH FORMULA

Abstract

We generalize several results on Chern–Simons models on Σ × S1in the so-called "torus gauge" which were obtained in [A. Hahn, An analytic approach to Turaev's shadow invariant, J. Knot Theory Ramifications17(11) (2008) 1327–1385] (= 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.