Simple supergravity, supersymmetric nonlinear gravitons and supertwistor theory

Abstract

A relationship between the geometry of the (4 mod 4)-dimensional superspace of N=1 supergravity, M, and the holomorphic structure of the (5 mod 2)-dimensional superspace of null supergeodesics, N, associated with M is investigated. An invariant definition of the local supertwistor bundle T on M is found, and it is proved that its dual graded skew square Lambda 2T* admits a non-zero horizontal section if and only if M is superconformally Einstein. A supersymmetric extension of LeBrun's Einstein bundle (1989) on N is constructed. The significance of this bundle stems from the fact that its non-vanishing holomorphic sections are in one-to-one correspondence with solutions of N=1, D=4 supergravity equations with cosmological constant. All these constructions are investigated in more detail in the category of self-dual superspaces of N=1 supergravity, and a supersymmetric generalization of Penrose's nonlinear graviton construction (1976) is obtained.