N=2超Riemann球的模空间
The moduli space of N=2 super-Riemann spheres with tubes
摘要：
在复超几何的框架内，以二维亏格零全纯N=2超共形域论为基础，定义了N=2超黎曼球面的模空间，其中球面具有定向有序的半无限管（或等价地，定向有序的穿孔，局部超共形坐标在穿孔处为零），模N=2超共形等价.我们发展了一个正式的理论无穷小N=2超共形变换的基础上表示的N=2 Neveu-Schwarz代数的超导子。特别地，通过这些无穷小，我们提出了N =2超黎曼球面的N = 2超投射变换的李群。我们用这些无穷小给出了模空间的一个重新表述。引入了带管的广义N=2超Riemann球，讨论了广义和非广义N=2超Riemann球的某些模空间的群结构.定义了对称群在模空间上的作用。最后讨论了N=2超共形结构的非齐次（相对于齐次）坐标系以及在此坐标系中的相应结果。
英文摘要：
Within the framework of complex supergeometry and motivated by two-dimensional genus-zero holomorphic N=2 superconformal field theory, we define the moduli space of N=2 super-Riemann spheres with oriented and ordered half-infinite tubes (or equivalently, oriented and ordered punctures, and local superconformal coordinates vanishing at the punctures), modulo N=2 superconformal equivalence. We develop a formal theory of infinitesimal N=2 superconformal transformations based on a representation of the N=2 Neveu-Schwarz algebra in terms of superderivations. In particular, via these infinitesimals we present the Lie supergroup of N=2 superprojective transformations of the N=2 super-Riemann sphere. We give a reformulation of the moduli space in terms of these infinitesimals. We introduce generalized N=2 super-Riemann spheres with tubes and discuss some group structures associated to certain moduli spaces of both generalized and non-generalized N=2 super-Riemann spheres. We define an action of the symmetric groups on the moduli space. Lastly we discuss the nonhomogeneous (versus homogeneous) coordinate system associated to N=2 superconformal structures and the corresponding results in this coordinate system.
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