Abstract
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.
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Assel, B., Martelli, D., Murthy, S. et al. Localization of supersymmetric field theories on non-compact hyperbolic three-manifolds. J. High Energ. Phys. 2017, 95 (2017). https://doi.org/10.1007/JHEP03(2017)095
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DOI: https://doi.org/10.1007/JHEP03(2017)095