Charged Conformal Killing Spinors

Abstract

We study the twistor equation on pseudo-Riemannian $Spi{n}^c-$manifolds whose solutions we call charged conformal Killing spinors (CCKS). We derive several integrability conditions for the existence of CCKS and study their relations to spinor bilinears. A construction principle for Lorentzian manifolds admitting CCKS with nontrivial charge starting from CR-geometry is presented. We obtain a partial classification result in the Lorentzian case under the additional assumption that the associated Dirac current is normal conformal and complete the Classification of manifolds admitting CCKS in all dimensions and signatures $\le 5$ which has recently been initiated in the study of supersymmetric field theories on curved space.

arXiv comment26 pages v2: typos corrected, minor changes

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Cited by in corpus (3)

• Supersymmetric gauge theories on five-manifolds
• Notes on Super Killing Tensors
• Gauged twistor spinors and symmetry operators