On rigid supersymmetry and notions of holomorphy in five dimensions

Abstract

We study the equations governing rigid N=1 supersymmetry in five dimensions. If the supersymmetry spinor satisfies a reality condition, these are foliations admitting families of almost complex structures on the leaves. In other words, all these manifolds have families of almost Cauchy-Riemann (CR) structures. After deriving integrability conditions under which circumstances the almost CR structure defines a CR manifold or a transversally holomorphic foliation (THF), we discuss implications on localization. We also discuss potential global obstructions to the existence of solutions.

14 pages; typos corrected; references added

References in corpus (6)

• Supersymmetric Gauge Theories on the Five-Sphere
• From Rigid Supersymmetry to Twisted Holomorphic Theories
• Supersymmetric gauge theories on squashed five-spheres and their gravity duals
• 5d Higgs Branch Localization, Seiberg-Witten Equations and Contact Geometry
• Partition functions for equivariantly twisted $\mathcal{N}=2$ gauge theories on toric Kähler manifolds
• Supersymmetrizing 5d instanton operators