Twistor Actions for Self-Dual Supergravities
Abstract
Description
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.
v2: 29 pages, substantially revised and rewritten with a clearer and more complete treatment, an extra 8 pages, replaced with version to appear in CMP
v2: 29 pages, substantially revised and rewritten with a clearer and more complete treatment, an extra 8 pages, replaced with version to appear in CMP