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Integrability conditions for Killing spinors

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Abstract

The conditions for the existence of solutions ofD µη=±cγµη are discussed. In general, it is not sufficient to consider only the first integrability condition [D µ,D v ]η=−2c 2γ{µv}η; in particular, the second integrability condition is needed to explain why, in certain cases, only for one choice of sign does a solution exist. The Killing spinor-tensors, as defined by Walker and Penrose, are shown to be the spinorial equivalent of conformal Killing tensors. Their relationship to the Killing spinors and spinor-vectors used in supergravity, is given.

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Authors and Affiliations

  1. Instituut voor Theoretische Fysica, Princetonplein 5, P.O. Box 80.006, NL-2508 TA, Utrecht, The Netherlands

    P. van Nieuwenhuizen

  2. California Institute of Technology, 91125, Pasadena, CA, USA

    N. P. Warner

Authors
  1. P. van Nieuwenhuizen
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  2. N. P. Warner
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Additional information

Communicated by S. W. Hawking

On leave from the Institute for Theoretical Physics of the State University of New York at Stony Brook

Work supported in part by the U.S. Department of Energy under Contract No. DEAC-03-81-ER 40050 and Weingart Fellowship

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van Nieuwenhuizen, P., Warner, N.P. Integrability conditions for Killing spinors. Commun.Math. Phys. 93, 277–284 (1984). https://doi.org/10.1007/BF01223747

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  • DOI: https://doi.org/10.1007/BF01223747

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