Twistor Actions for Self-dual Supergravities

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 Rsymmetry 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 ∂̄-operator on a supertwistor space, i.e., on regions in CP3|8. For N = 0, we also give a formulation that does not require the choice of a background.