1208.1724 (Brendan McLellan)

Localization in Abelian Chern-Simons Theory    [PDF]

Brendan McLellan

Chern-Simons theory on a closed contact three-manifold is studied when the Lie group for gauge transformations is compact, connected and abelian. A rigorous definition of an abelian Chern-Simons partition function is derived using the Faddeev-Popov gauge fixing method. A symplectic abelian Chern-Simons partition function is also derived using the technique of non-abelian localization. An identification of the symplectic abelian partition function with the abelian Chern-Simons partition function as a rigorous topological three-manifold invariant is established up to phase. 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.

View original: http://arxiv.org/abs/1208.1724