Open Access
January 2013 Localization for Wilson Loops in Chern–Simons Theory
Chris Beasely
Adv. Theor. Math. Phys. 17(1): 1-240 (January 2013).


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.


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Chris Beasely. "Localization for Wilson Loops in Chern–Simons Theory." Adv. Theor. Math. Phys. 17 (1) 1 - 240, January 2013.


Published: January 2013
First available in Project Euclid: 29 July 2013

MathSciNet: MR3066489

Rights: Copyright © 2013 International Press of Boston

Vol.17 • No. 1 • January 2013
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