Localization in Abelian Chern-Simons Theory

Understand

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.
• This physically identifies the symplectic abelian partition function with the abelian Chern-Simons partition function as rigorous topological three-manifold invariants.