Twistors and antipodes in de Sitter space

Abstract

We develop the basics of twistor theory in de Sitter space, up to the Penrose transform for free massless fields. We treat de Sitter space as fundamental, as one does for Minkowski space in conventional introductions to twistor theory. This involves viewing twistors as spinors of the de Sitter group SO(4,1). When attached to a spacetime point, such a twistor can be reinterpreted as a local SO(3,1) Dirac spinor. Our approach highlights the antipodal map in de Sitter space, which gives rise to doublings in the standard relations between twistors and spacetime. In particular, one can generate a field with both handedness signs from a single twistor function. Such fields naturally live on antipodally-identified de Sitter space dS_4/Z_2, which has been put forward as the ideal laboratory for quantum gravity with positive cosmological constant.

27 pages; v2: standardized normalization conventions between different papers

References in corpus (3)

• The Amplituhedron
• A Measure of de Sitter Entropy and Eternal Inflation
• Twistor Strings for N=8 Supergravity

Cited by in corpus (6)

• Spinor-helicity variables for cosmological horizons in de Sitter space
• Higher-spin symmetry vs. boundary locality, and a rehabilitation of dS/CFT
• The holographic dual of the Penrose transform
• Higher-spin gravity as a theory on a fixed (anti) de Sitter background
• Antipodally symmetric gauge fields and higher-spin gravity in de Sitter space
• Holographic quantization of linearized higher-spin gravity in the de Sitter causal patch