摘要翻译：
证明了紧Calabi-Yau三元上的开拓扑弦振幅满足Bershadsky、Cecotti、Ooguri和Vafa的全纯反常方程的推广。D-膜构型的总拓扑电荷必须消失才能满足蝌蚪对消。这类D-膜的边界态是由Hodge理论正规函数全纯捕获的。它的Griffiths无穷小不变量类似于闭弦Yukawa耦合，在含D-膜拓扑弦的Feynman图展开中起着终止符的作用。求解了全纯异常方程，确定了实五次上一些具有代表性的低亏格少边界世界片的全纯模糊度。
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英文标题：
《Extended Holomorphic Anomaly and Loop Amplitudes in Open Topological
  String》
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作者：
Johannes Walcher
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最新提交年份：
2009
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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：
  Open topological string amplitudes on compact Calabi-Yau threefolds are shown to satisfy an extension of the holomorphic anomaly equation of Bershadsky, Cecotti, Ooguri and Vafa. The total topological charge of the D-brane configuration must vanish in order to satisfy tadpole cancellation. The boundary state of such D-branes is holomorphically captured by a Hodge theoretic normal function. Its Griffiths' infinitesimal invariant is the analogue of the closed string Yukawa coupling and plays the role of the terminator in a Feynman diagram expansion for the topological string with D-branes. The holomorphic anomaly equation is solved and the holomorphic ambiguity is fixed for some representative worldsheets of low genus and with few boundaries on the real quintic.
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PDF链接：
https://arxiv.org/pdf/0705.4098