Selfdual supergravity and twistor theory
Abstract
By generalizing and extending some of the earlier results derived by Manin and Merkulov, a twistor description is given of fourdimensional {{\mathcal N}} extended (gauged) selfdual supergravity with and without cosmological constant. Starting from the category of (44{{\mathcal N}}) dimensional complex superconformal supermanifolds, the categories of (42{{\mathcal N}}) dimensional complex quaternionic, quaternionic Kähler and hyperKähler rightchiral supermanifolds are introduced and discussed. We then present a detailed twistor description of these types of supermanifolds. In particular, we construct supertwistor spaces associated with complex quaternionic rightchiral supermanifolds, and explain what additional supertwistor data allow for giving those supermanifolds a hyperKähler structure. In this way, we obtain a supersymmetric generalization of Penrose's nonlinear graviton construction. We furthermore give an alternative formulation in terms of a supersymmetric extension of LeBrun's Einstein bundle. This allows us to include the cases with nonvanishing cosmological constant. We also discuss the bundle of local supertwistors and address certain implications thereof. Finally, we comment on a real version of the theory related to Euclidean signature.
 Publication:

Classical and Quantum Gravity
 Pub Date:
 December 2007
 DOI:
 10.1088/02649381/24/24/010
 arXiv:
 arXiv:0705.1422
 Bibcode:
 2007CQGra..24.6287W
 Keywords:

 High Energy Physics  Theory;
 Mathematical Physics
 EPrint:
 v3: 1+47 pages, typos corrected, references and minor clarifications added, replaced with published version