Twistor Actions for Self-Dual Supergravities
High Energy Physics - Theory
2009-04-17 v2 General Relativity and Quantum Cosmology
Mathematical Physics
Differential Geometry
math.MP
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.
Cite
@article{arxiv.0706.1941,
title = {Twistor Actions for Self-Dual Supergravities},
author = {Lionel J. Mason and Martin Wolf},
journal= {arXiv preprint arXiv:0706.1941},
year = {2009}
}