Localization on three-manifolds

TY - JOUR

T1 - Localization on three-manifolds

AU - Alday, Luis F.

AU - Martelli, Dario

AU - Richmond, Paul

AU - Sparks, James

PY - 2013/10

Y1 - 2013/10

N2 - 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 formula agrees with a recently discovered two-parameter family of dual supergravity solutions. We also explain how our results may be applied to prove vortex-antivortex factorization. Finally, we comment on the extension of our results to three-manifolds with non-trivial fundamental group.

AB - 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 formula agrees with a recently discovered two-parameter family of dual supergravity solutions. We also explain how our results may be applied to prove vortex-antivortex factorization. Finally, we comment on the extension of our results to three-manifolds with non-trivial fundamental group.

KW - Chern-Simons Theories

KW - Supersymmetric gauge theory

UR - http://www.scopus.com/inward/record.url?scp=84892631459&partnerID=8YFLogxK

U2 - 10.1007/JHEP10(2013)095

DO - 10.1007/JHEP10(2013)095

M3 - Article

AN - SCOPUS:84892631459

SN - 1126-6708

VL - 2013

JO - Journal of High Energy Physics

JF - Journal of High Energy Physics

IS - 10

M1 - 95

ER -