【摘要】 杂化弦的共形不变性和超共形不变性可用圈和超圈的微分同胚群 DiffS~1和Super-DiffS~1描述.基圈的重参数化形成商空间 M=DiffS~1/S~1和N=Super—DiffS~1/S~1.它们是无限维的 Kahler 流形和超 Kahler 流形.本文研究这些无限维流形的全纯几何.用陪集空间的技术讨论了它们的辛结构,通过在 M 和 N 上引入全纯坐标和夏结构我们计算了在原点邻域内的 Killing 矢量,给出了 M 和 N 上的Riemann 度规.这些结果在研究杂化弦的共形反常时有用.更多还原

【Abstract】 Conformal invariances of heterotic string can be described by the groups of diffeomorphisms of the circle and super-circle,DiffS~l and Super-DiffS~l.The reparametrizations of the loop and super-loop from the quotient spaces M=DiffS~l/S~l and N=Super-DiffS~l/S~l.In this paper,it is shown that M and N are infinite dimensional Kahler and super-Kahler manifolds,respectively,and the author studies the holomorphic geometry of these manifolds,and investigates their sympletic structures by using the coset space techniques.Then,this paper computes explicitly the Killing Vectors in the neighborhood of the origin,and constructs the associated Riemannian metrics by introducing the holomorphie coordinates and the complex struc- tures on these manifolds.更多还原