1206.0439 (Atle Hahn)

From simplicial Chern-Simons theory to the shadow invariant I    [PDF]

Atle Hahn

This is the first of a series of papers in which we develop a "discretization approach" for the rigorous realization of the non-Abelian Chern-Simons path integral for manifolds M of the form M=Sigma x S1 and arbitrary simply-connected compact structure groups G. More precisely, we will introduce, for general links L in M, a rigorous version WLO_{rig}(L) of (the expectation values of) the corresponding Wilson loop observable WLO(L) in the so-called "torus gauge" by Blau and Thompson (Nucl. Phys. B408(1):345-390, 1993). For a simple class of links L we then evaluate WLO_{rig}(L) explicitly in a non-perturbative way, finding agreement with Turaev's shadow invariant |L|.

View original: http://arxiv.org/abs/1206.0439