Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1993-04-21
J.Diff.Geom. 39 (1994) 173-213
Physics
High Energy Physics
High Energy Physics - Theory
40 pages
Scientific paper
In a previous paper [\AS], we used superspace techniques to prove that perturbation theory (around a classical solution with no zero modes) for Chern--Simons quantum field theory on a general $3$-manifold $M$ is finite. We conjectured (and proved for the case of $2$-loops) that, after adding counterterms of the expected form, the terms in the perturbation theory define topological invariants. In this paper we prove this conjecture. Our proof uses a geometric compactification of the region on which the Feynman integrand of Feynman diagrams is smooth as well as an extension of the basic propagator of the theory.
Axelrod Scott
Singer I. M.
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