Twistor Actions for Self-Dual Supergravities

TL;DR

This paper develops holomorphic Chern-Simons-like actions on supertwistor space for self-dual supergravity theories with varying supersymmetries, R-symmetry gaugings, and cosmological constants, providing a unified twistor framework.

Contribution

It introduces a novel supertwistor space formulation for self-dual supergravity theories applicable to N=0 to 8 supersymmetries, including cases with gauged R-symmetry and cosmological constant.

Findings

Formulation of supertwistor actions for various supersymmetries.

Representation of R-symmetry gauging via Poisson structures.

Background-independent formulation for N=0 supergravity.

Abstract

We give holomorphic Chern-Simons-like action functionals on supertwistor space for self-dual supergravity theories in four dimensions, dealing with N=0,...,8 supersymmetries, the cases where different parts of the R-symmetry are gauged, and with or without a cosmological constant. The gauge group is formally the group of holomorphic Poisson transformations of supertwistor space where the form of the Poisson structure determines the amount of R-symmetry gauged and the value of the cosmological constant. We give a formulation in terms of a finite deformation of an integrable \dbar-operator on a supertwistor space, i.e., on regions in CP^{3|8}. For N=0, we also give a formulation that does not require the choice of a background.