Supersymmetric gauge theories on five-manifolds

Abstract

We construct rigid supersymmetric gauge theories on Riemannian five-manifolds. We follow a holographic approach, realizing the manifold as the conformal boundary of a six-dimensional bulk supergravity solution. This leads to a systematic classification of five-dimensional supersymmetric backgrounds with gravity duals. We show that the background metric is furnished with a conformal Killing vector, which generates a transversely holomorphic foliation with a transverse Hermitian structure. Moreover, we prove that any such metric defines a supersymmetric background. Finally, we construct supersymmetric Lagrangians for gauge theories coupled to arbitrary matter on such backgrounds.

35 pages: v2: minor corrections and references added. Published version

References in corpus (10)

• 5-dim Superconformal Index with Enhanced En Global Symmetry
• Supersymmetric Gauge Theories on the Five-Sphere
• Supersymmetric gauge theories on squashed five-spheres and their gravity duals
• Supersymmetric Rényi Entropy in Five Dimensions
• The gravity dual of supersymmetric gauge theories on a squashed five-sphere
• The holographic supersymmetric Renyi entropy in five dimensions
• Gluing Nekrasov partition functions
• 5d Higgs Branch Localization, Seiberg-Witten Equations and Contact Geometry
• Supersymmetric backgrounds from 5d N=1 supergravity
• Charged Conformal Killing Spinors

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