Advances in Theoretical and Mathematical Physics

Localization for Wilson Loops in Chern–Simons Theory

Chris Beasely

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We reconsider Chern–Simons gauge theory on a Seifert manifold $M$, which is the total space of a non-trivial circle bundle over a Riemann surface $\Sigma$, 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 that wrap the circle fibers of $M$ over $\Sigma$. 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 in $S^3$, an observation made empirically by Lawrence and Rozansky prior to this work.

Article information

Adv. Theor. Math. Phys., Volume 17, Number 1 (2013), 1-240.

First available in Project Euclid: 29 July 2013

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Beasely, Chris. Localization for Wilson Loops in Chern–Simons Theory. Adv. Theor. Math. Phys. 17 (2013), no. 1, 1--240.

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