### 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.

Original language | English (US) |
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Pages (from-to) | 1103-1117 |

Number of pages | 15 |

Journal | Journal of High Energy Physics |

Volume | 8 |

Issue number | 12 |

State | Published - Dec 1 2004 |

Externally published | Yes |

### Keywords

- Conformal and W Symmetry
- Field Theories in Higher Dimensions

### ASJC Scopus subject areas

- Nuclear and High Energy Physics

### Cite this

*Journal of High Energy Physics*,

*8*(12), 1103-1117.