7 research outputs found
Higher-Dimensional Twistor Transforms using Pure Spinors
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.Comment: 17 pages harvmac tex. Modified title, abstract, introduction and
references to acknowledge earlier papers by Hughston and other