Localization in abelian Chern-Simons theory

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  • Brendan Donald Kenneth McLellan, Denmark
Chern-Simons theory on a closed contact three-manifold is studied when the Lie group for gauge transformations is compact, connected, and abelian. The abelian Chern-Simons partition function is derived using the Faddeev-Popov gauge fixing method. The partition function is then formally computed using the technique of non-abelian localization. This study leads to a natural identification of the abelian Reidemeister-Ray-Singer torsion as a specific multiple of the natural unit symplectic volume form on the moduli space of flat abelian connections for the class of Sasakian three-manifolds. The torsion part of the abelian Chern-Simons partition function is computed explicitly in terms of Seifert data for a given Sasakian three-manifold.
Original languageEnglish
JournalJournal of Mathematical Physics
Volume54
Issue2
Pages (from-to)023507
Number of pages24
ISSN0022-2488
DOIs
Publication statusPublished - 11 Feb 2013

    Research areas

  • Chern-Simons theory, Contact Geometry, Quantum Topology, Path Integral, Non-abelian localization

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