Localization for Wilson Loops in Chern-Simons Theory

Understand

We reconsider Chern-Simons gauge theory on a Seifert manifold M, which is the total space of a nontrivial circle bundle over a Riemann surface, possibly with orbifold points.

• As shown in previous work with Witten, the path integral technique of non-abelian localization can be used to express the partition function of Chern-Simons theory in terms of the equivariant cohomology of the moduli space of flat connections on M.
• Here we extend this result to apply to the expectation values of Wilson loop operators which wrap the circle fibers of M.
• Under localization, such a Wilson loop operator reduces naturally to the Chern character of an associated universal bundle over the moduli space.