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arXiv · 1504.00321

On rigid supersymmetry and notions of holomorphy in five dimensions

Yiwen Pan·Johannes Schmude
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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.

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Yiwen Pan, Johannes Schmude. 2015-06-01. On rigid supersymmetry and notions of holomorphy in five dimensions. https://arxiv.org/abs/1504.00321

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