Non-abelian localization for chern-simons theory

Chris Beasley, Edward Witten

Research output: Contribution to journalArticlepeer-review

78 Scopus citations

Abstract

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 Rozan-sky 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.

Original languageEnglish (US)
Pages (from-to)183-323
Number of pages141
JournalJournal of Differential Geometry
Volume70
Issue number2
DOIs
StatePublished - 2005

All Science Journal Classification (ASJC) codes

  • Analysis
  • Algebra and Number Theory
  • Geometry and Topology

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