N=1个带管超球的模空间及缝合运算
The moduli space of N=1 superspheres with tubes and the sewing operation
摘要：
在复超几何的框架下，以二维零亏格全纯N=1超共形域论为理论基础，定义了N=1亏格零超黎曼曲面的模空间，曲面具有定向有序半无限管，模超共形等价.我们在这个模空间上定义了一个缝纫操作，它产生了缝纫方程、归一化条件和边界条件。为了解决这个方程，我们开发了一个正式的理论无穷小N=1超共形变换的基础上表示的N=1的Neveu-Schwarz代数的超导子。我们解决了一个正式版本的缝纫方程，证明了一个身份的某些指数的superderivatives涉及无穷多个正式的变量。我们使用这些正式的结果给出了一个重新制定的模空间，更详细的描述的缝纫操作，和一个明确的公式，用于获得一个典型的超球与管从缝纫在一起的两个典型的超球与管。我们给出了一些具体的例子缝纫，其中两个给出了几何类似物的结合N=1的Neveu-Schwarz顶点算子超代数。研究了在具有1+1管（一个输出管和一个输入管）的超球面的模空间单位元上的亚纯切空间中的一个线性泛函，该线性泛函与N = 1的Neveu-Schwarz顶点算子超代数中的N= 1的Neveu-Schwarz元相关联.我们证明了缝纫操作所产生的无穷级数的解析性和收敛性。最后，在具有1+1管的超球面的切空间空间的恒等式上定义了一个括号，并证明了这给出了中心电荷为零的N=1 Neveu-Schwarz代数的一个表示.
英文摘要：
Within the framework of complex supergeometry and motivated by two-dimensional genus-zero holomorphic N=1 superconformal field theory, we define the moduli space of N=1 genus-zero super-Riemann surfaces with oriented and ordered half-infinite tubes, modulo superconformal equivalence. We define a sewing operation on this moduli space which gives rise to the sewing equation and normalization and boundary conditions. To solve this equation, we develop a formal theory of infinitesimal N=1 superconformal transformations based on a representation of the N=1 Neveu-Schwarz algebra in terms of superderivations. We solve a formal version of the sewing equation by proving an identity for certain exponentials of superderivations involving infinitely many formal variables. We use these formal results to give a reformulation of the moduli space, a more detailed description of the sewing operation, and an explicit formula for obtaining a canonical supersphere with tubes from the sewing together of two canonical superspheres with tubes. We give some specific examples of sewings, two of which give geometric analogues of associativity for an N=1 Neveu-Schwarz vertex operator superalgebra. We study a certain linear functional in the supermeromorphic tangent space at the identity of the moduli space of superspheres with 1+1 tubes (one outgoing tube and one incoming tube) which is associated to the N=1 Neveu-Schwarz element in an N=1 Neveu-Schwarz vertex operator superalgebra. We prove the analyticity and convergence of the infinite series arising from the sewing operation. Finally, we define a bracket on the supermeromorphic tangent space at the identity of the moduli space of superspheres with 1+1 tubes and show that this gives a representation of the N=1 Neveu-Schwarz algebra with central charge zero.
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