Non-Abelian Localization For Chern-Simons Theory

Details Non-Abelian Localization For Chern-Simons Theory Non-Abelian Localization For Chern-Simons Theory

2005-03-16

arxiv.org/abs/hep-th/0503126v2

J.Diff.Geom.70:183-323,2005

Physics

High Energy Physics

High Energy Physics - Theory

131 pages, harvmac, v2: references added

Scientific paper

We reconsider Chern-Simons gauge theory on a Seifert manifold M (the total space of a nontrivial circle bundle over a Riemann surface). When M is a Seifert manifold, Lawrence and Rozansky have shown from the exact solution of Chern-Simons theory that the partition function has a remarkably simple structure and can be rewritten entirely as a sum of local contributions from the flat connections on M. We explain how this empirical fact follows from the technique of non-abelian localization as applied to the Chern-Simons path integral. In the process, we show that the partition function of Chern-Simons theory on M admits a topological interpretation in terms of the equivariant cohomology of the moduli space of flat connections on M.

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