Open Access
June 2005 Non-Abelian localization for Chern-Simons theory
Chris Beasley, Edward Witten
J. Differential Geom. 70(2): 183-323 (June 2005). DOI: 10.4310/jdg/1143642932


We reconsider Chern-Simons gauge theory on a Seifert manifold M (the total space of a nontrivial circle bundle over a Riemann surface Σ). 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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Chris Beasley. Edward Witten. "Non-Abelian localization for Chern-Simons theory." J. Differential Geom. 70 (2) 183 - 323, June 2005.


Published: June 2005
First available in Project Euclid: 29 March 2006

zbMATH: 1097.58012
MathSciNet: MR2192257
Digital Object Identifier: 10.4310/jdg/1143642932

Rights: Copyright © 2005 Lehigh University

Vol.70 • No. 2 • June 2005
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