论文标题
超符合的几何形状和本地扭曲器
Superconformal geometries and local twistors
论文作者
论文摘要
时空尺寸中的超符合几何形状$ d = 3,4，{5} $和$ 6 $，根据本地超级翼斯托捆绑包，而不是标准超级空间。这些在矩阵价值的一型矩阵中，这些纳塔式接纳的超符号连接。为了与标准的超空间形式主义接触，表明人们总是可以选择连接和曲率的比例部分消失的仪表，在这种情况下，共形和$ s $ subsymmetraly-metralymetraly Transformations将其汇总到超级 - 韦尔特变换中。通过施加约束，可以将组件字段的数量减少到最小脱壳共形超重力多重多重次数的数量，这些约束在大多数情况下仅包括将均匀的协变量扭转两种形式消失。必须通过$ d = 3,4 $的最大情况来补充这一点。还从最小的角度讨论了该主题，其中仅引入尺寸零扭转。最后，我们介绍了一类新的超级曼尼福德，当地的超级格拉斯曼尼亚人，为超宪法理论提供了另一种环境。
Superconformal geometries in spacetime dimensions $D=3,4,{5}$ and $6$ are discussed in terms of local supertwistor bundles over standard superspace. These natually admit superconformal connections as matrix-valued one-forms. In order to make contact with the standard superspace formalism it is shown that one can always choose gauges in which the scale parts of the connection and curvature vanish, in which case the conformal and $S$-supersymmetry transformations become subsumed into super-Weyl transformations. The number of component fields can be reduced to those of the minimal off-shell conformal supergravity multiplets by imposing constraints which in most cases simply consists of taking the even covariant torsion two-form to vanish. This must be supplemented by further dimension-one constraints for the maximal cases in $D=3,4$. The subject is also discussed from a minimal point of view in which only the dimension-zero torsion is introduced. Finally, we introduce a new class of supermanifolds, local super Grassmannians, which provide an alternative setting for superconformal theories.
