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arXiv · hep-th/0409243

Higher-Dimensional Twistor Transforms using Pure Spinors

Nathan Berkovits·Sergey A. Cherkis
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Abstract

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 R^{2n}. For d=4 and d=6, these spaces are CP^1 and CP^3, 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.

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Nathan Berkovits, Sergey A. Cherkis. 2004-11-16. Higher-Dimensional Twistor Transforms using Pure Spinors. https://doi.org/10.1088/1126-6708%2F2004%2F12%2F049

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