标题： 自对偶超重力与扭量理论 显示英文标题

标题： Self-Dual Supergravity and Twistor Theory

摘要： 通过推广和扩展Manin和Merkulov早先得出的一些结果，给出了四维N-扩展（规范）自对偶超引力的扭子描述，包括有和没有宇宙学常数的情况。 从(4|4N)维复超共形超流形的范畴出发，引入并讨论了(4|2N)维复四元数、四元数凯勒和超凯勒右旋超流形的范畴。 然后，我们详细地给出了这些类型超流形的扭子描述。 特别是，我们构造了与复四元数右旋超流形相关的超扭子空间，并解释了哪些额外的超扭子数据允许这些超流形具有超凯勒结构。 通过这种方式，我们得到了Penrose非线性引力子构造的超对称推广。 我们还给出了一个替代表述，即LeBrun爱因斯坦束的超对称扩展。 这使我们能够包含宇宙学常数不为零的情况。 我们还讨论了局部超扭子的丛并涉及其某些含义。 最后，我们评论了与欧几里得符号相关的理论的实数版本。 显示英文摘要

摘要： By generalizing and extending some of the earlier results derived by Manin and Merkulov, a twistor description is given of four-dimensional N-extended (gauged) self-dual supergravity with and without cosmological constant. Starting from the category of (4|4N)-dimensional complex superconformal supermanifolds, the categories of (4|2N)-dimensional complex quaternionic, quaternionic Kaehler and hyper-Kaehler 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 allows for giving those supermanifolds a hyper-Kaehler 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.