Article,
Localization for Wilson Loops in Chern-Simons Theory
(May 12, 2010)
Abstract
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. Along
the way, we demonstrate that the stationary-phase approximation to the Wilson
loop path integral is exact for torus knots, an observation made empirically by
Lawrence and Rozansky prior to this work.
