Friday, July 26, 2013

1307.6848 (Luis F. Alday et al.)

Localization on Three-Manifolds    [PDF]

Luis F. Alday, Dario Martelli, Paul Richmond, James Sparks
We consider supersymmetric gauge theories on Riemannian three-manifolds with the topology of a three-sphere. The three-manifold is always equipped with a contact structure and an associated Reeb vector field. We show that the partition function depends only on this vector field, giving an explicit expression in terms of the double sine function. In the large N limit our result agrees with a recently discovered two-parameter family of dual supergravity solutions. We also comment on the extension of our results to three-manifolds with non-trivial fundamental group.
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