Localization of supersymmetric field theories on non-compact hyperbolic three-manifolds

Benjamin Assel*, Dario Martelli, Sameer Murthy, Daisuke Yokoyama

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

15 Citations (Scopus)
141 Downloads (Pure)


We study supersymmetric gauge theories with an R-symmetry, defined on non-compact, hyperbolic, Riemannian three-manifolds, focusing on the case of a supersymmetry-preserving quotient of Euclidean AdS3. We compute the exact partition function in these theories, using the method of localization, thus reducing the problem to the computation of one-loop determinants around a supersymmetric locus. We evaluate the one-loop determinants employing three different techniques: an index theorem, the method of pairing of eigenvalues, and the heat kernel method. Along the way, we discuss aspects of supersymmetry in manifolds with a conformal boundary, including supersymmetric actions and boundary conditions.

Original languageEnglish
Article number95
Number of pages64
JournalJournal of High Energy Physics
Issue number3
Publication statusPublished - 17 Mar 2017


  • Chern-Simons Theories
  • Field Theories in Lower Dimensions
  • Supersymmetric Gauge Theory


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