Higher-Dimensional Twistor Transforms using Pure Spinors

Nathan Berkovits, Sergey A Cherkis
2004 Journal of High Energy Physics  
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
more » ... stor transform for d>6 when the pure spinor satisfies nonlinear constraints, and present explicit formulas for solutions of the massless field equations.
doi:10.1088/1126-6708/2004/12/049 fatcat:bonsh673yzfipbux6qufyp2t44