Localization on three-manifolds

Luis F. Alday, Dario Martelli, Paul Richmond, James Sparks

Research output: Contribution to journalArticlepeer-review

69 Citations (Scopus)


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.
Original languageEnglish
Article number95
JournalJournal of High Energy Physics
Issue number10
Publication statusPublished - Oct 2013


  • Chern-Simons Theories
  • Supersymmetric gauge theory


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