# Pure Spinors are Higher-Dimensional Twistors

**Source**: https://www.maths.tcd.ie/report_series/abstracts/tcdm0416.html
**Parent**: https://www.maths.tcd.ie/research/papers/

**Pure Spinors are Higher-Dimensional Twistors**

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 corresponding pure spinors have been interpreted as four
and six-dimensional twistor variables. In this paper, we argue that the
identification of pure spinors and twistors holds in any even dimension,
and we use pure spinors to construct massless solutions in higher
dimensions.