Rigid Supersymmetry from Conformal Supergravity in Five Dimensions

Abstract

We study the rigid limit of 5d conformal supergravity with minimal supersymmetry on Riemannian manifolds. The necessary and sufficient condition for the existence of a solution is the existence of a conformal Killing vector. Whenever a certain $SU(2)$ curvature becomes abelian the backgrounds define a transversally holomorphic foliation. Subsequently we turn to the question under which circumstances these backgrounds admit a kinetic Yang-Mills term in the action of a vector multiplet. Here we find that the conformal Killing vector has to be Killing. We supplement the discussion with various appendices.

23 pages

References in corpus (13)

• 5-dim Superconformal Index with Enhanced En Global Symmetry
• Supersymmetric Gauge Theories on the Five-Sphere
• The Invar tensor package: Differential invariants of Riemann
• Instanton operators and symmetry enhancement in 5d supersymmetric gauge theories
• Instanton Operators in Five-Dimensional Gauge Theories
• 5d Higgs Branch Localization, Seiberg-Witten Equations and Contact Geometry
• Supersymmetric gauge theories on five-manifolds
• Supersymmetric backgrounds from 5d N=1 supergravity
• Instanton operators and symmetry enhancement in 5d supersymmetric USp, SO and exceptional gauge theories
• Super-Yang-Mills theories on S4 x R
• Supersymmetrizing 5d instanton operators
• The geometric Langlands twist in five and six dimensions
• On rigid supersymmetry and notions of holomorphy in five dimensions

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• The NS limit of the 5D Superconformal Index
• Proving the 6d Cardy Formula and Matching Global Gravitational Anomalies
• Self-consistency of Conformally Coupled ABJM Theory at the Quantum Level
• Supersymmetric Yang-Mills theory on conformal supergravity backgrounds in ten dimensions