Higher-dimensional twistor transforms using pure spinors

Nathan Berkovits, Sergey A. Cherkis

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31 Scopus citations


Hughston has shown that projective pure spinors can be used to construct massless solutions in higher dimensions, generalizing the four-dimensional twistor transform of Penrose. In any even (euclidean) dimension d = 2n, projective pure spinors parameterize the coset space SO(2n)/U(n), which is the space of all complex structures on ℝ2n. For d = 4 and d = 6, these spaces are ℂℙ1 and ℂℙ3 and the appropriate twistor transforms can easily be constructed. In this paper, we show how to construct the twistor transform for d > 6 when the pure spinor satisfies nonlinear constraints, and present explicit formulas for solutions of the massless field equations.

Original languageEnglish (US)
Pages (from-to)1103-1117
Number of pages15
JournalJournal of High Energy Physics
Issue number12
StatePublished - Dec 1 2004


  • Conformal and W Symmetry
  • Field Theories in Higher Dimensions

ASJC Scopus subject areas

  • Nuclear and High Energy Physics

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