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摘要翻译：
本文证明了Cacciatori、Dalla Piazza和van Geemen提出的三环手征超弦测度ansatz的两点函数消失。我们的证明使用了ansatz关于偶数陪集、theta函数的重新表述，特别是van Geemen和van der Geer在Jacobians上引入的$\gamma_{00}$线性系统的理论。在由D'Hoker和Phong计算振幅的二回路水平上，我们给出了由他们证明的两点函数消失的一个新的证明。我们还讨论了在更高属中证明所提出的ansatz的两点函数消失的可能方法。
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英文标题：
《The vanishing of two-point functions for three-loop superstring
scattering amplitudes》
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作者：
Samuel Grushevsky, Riccardo Salvati Manni
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最新提交年份：
2008
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分类信息：
一级分类：Physics 物理学
二级分类：High Energy Physics - Theory 高能物理-理论
分类描述：Formal aspects of quantum field theory. String theory, supersymmetry and supergravity.
量子场论的形式方面。弦理论，超对称性和超引力。
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一级分类：Mathematics 数学
二级分类：Algebraic Geometry 代数几何
分类描述：Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology
代数簇，叠，束，格式，模空间，复几何，量子上同调
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英文摘要：
In this paper we show that the two-point function for the three-loop chiral superstring measure ansatz proposed by Cacciatori, Dalla Piazza, and van Geemen vanishes. Our proof uses the reformulation of ansatz in terms of even cosets, theta functions, and specifically the theory of the $\Gamma_{00}$ linear system on Jacobians introduced by van Geemen and van der Geer. At the two-loop level, where the amplitudes were computed by D'Hoker and Phong, we give a new proof of the vanishing of the two-point function (which was proven by them). We also discuss the possible approaches to proving the vanishing of the two-point function for the proposed ansatz in higher genera.
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PDF链接：
https://arxiv.org/pdf/0806.0354
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