Higher-Dimensional Twistor Transforms using Pure Spinors
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.
Keywords
Cite
@article{arxiv.hep-th/0409243,
title = {Higher-Dimensional Twistor Transforms using Pure Spinors},
author = {Nathan Berkovits and Sergey A. Cherkis},
journal= {arXiv preprint arXiv:hep-th/0409243},
year = {2008}
}
Comments
17 pages harvmac tex. Modified title, abstract, introduction and references to acknowledge earlier papers by Hughston and others