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Charged conformal Killing spinors. (English) Zbl 1309.83077

Summary: We study the twistor equation on pseudo-Riemannian \(\mathrm{Spin}^{c}\)-manifolds whose solutions we call charged conformal Killing spinors (CCKSs). 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 \(\leq5\) which has recently been initiated in the study of supersymmetric field theories on curved space.{
©2015 American Institute of Physics}

MSC:

83C60 Spinor and twistor methods in general relativity and gravitational theory; Newman-Penrose formalism
83C22 Einstein-Maxwell equations
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