论文标题
对三个循环超弦振幅的边界贡献
Boundary contributions to three loop superstring amplitudes
论文作者
论文摘要
在II型超音理论中，给定环路订单$ g $的真空振幅可以从压缩的，$ g $ g $ supermoduli曲线$ \ overline {\ mathfrak m} _g $的边界中获得贡献。这些贡献捕获了振幅的长距离或红外行为。边界参数是$ g $超级黎曼表面的退化。然后，超模型空间对减少空间的全体形态投影将提供一种整合全体形态，超曲措施的方法，从而以$ g $ - 环的订单提供超音真空振幅。但是，这种投影通常不存在于较高属的大部分超模型空间上。然而，某些边界除数中的某些边界除法\ partial \ edline {\ mathfrak m} _g $ $可以全态形成在与通用形态的构图后，将其映射到骨气空间上，从而在此处启用全体形态的超态，超级编号。利用边界附近的SuperString度量的ANSATZ分解，我们的分析表明，对三个环真空振幅的边界贡献将消失在封闭的封闭式II型SuperString理论中，并具有不间断的空间超对称性。
In type II superstring theory, the vacuum amplitude at a given loop order $g$ can receive contributions from the boundary of the compactified, genus $g$ supermoduli space of curves $\overline{\mathfrak M}_g$. These contributions capture the long distance or infrared behaviour of the amplitude. The boundary parametrises degenerations of genus $g$ super Riemann surfaces. A holomorphic projection of the supermoduli space onto its reduced space would then provide a way to integrate the holomorphic, superstring measure and thereby give the superstring vacuum amplitude at $g$-loop order. However, such a projection does not generally exist over the bulk of the supermoduli spaces in higher genera. Nevertheless, certain boundary divisors in $\partial\overline{\mathfrak M}_g$ may holomorphically map onto a bosonic space upon composition with universal morphisms, thereby enabling an integration of the holomorphic, superstring measure here. Making use of ansatz factorisations of the superstring measure near the boundary, our analysis shows that the boundary contributions to the three loop vacuum amplitude will vanish in closed oriented type II superstring theory with unbroken spacetime supersymmetry.
