2007/05/31 by Martin Wolf · 2 citations
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Noncommutative and Quantum Gravity Theories #hep-th #math-ph #math.MP
paper · pdf · doi:10.1088/0264-9381/24/24/010
published as Class.Quant.Grav.24:6287-6328,2007 · v3: 1+47 pages, typos corrected, references and minor clarifications added, replaced with published version
arxiv created 2007/11/20 · openalex publication_date 2007/11/29 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30
By generalizing and extending some of the earlier results derived by Manin and Merkulov, a twistor description is given of four-dimensional -extended (gauged) self-dual supergravity with and without cosmological constant. Starting from the category of -dimensional complex superconformal supermanifolds, the categories of -dimensional complex quaternionic, quaternionic Kähler and hyper-Kähler right-chiral 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 right-chiral supermanifolds, and explain what additional supertwistor data allow for giving those supermanifolds a hyper-Kähler 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.