Hints for Off-Shell Mirror Symmetry in type II/F-theory Compactifications
Hints for Off-Shell Mirror Symmetry in type II/F-theory Compactifications
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DOI：
10.1016/j.nuclphysb.2010.06.017
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发表时间：
2009-09
期刊：
影响因子：
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通讯作者：
M. Alim;M. Hecht;H. Jockers;P. Mayr;A. Mertens;M. Soroush
中科院分区：
文献类型：
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作者：
M. Alim;M. Hecht;H. Jockers;P. Mayr;A. Mertens;M. Soroush
本文对紧Calabi-Yau流形上的D-膜在II型紧化和F-理论紧化中的参数依赖族进行了Hodge理论研究。从B-型膜的几何Gauss-Manin联络出发，研究了B-型膜的可积性和平坦性条件。B模型几何定义了一个有趣的算子环结构。对于镜像A模型，这表明存在所谓的A模型连接的开弦扩展，而发现的环结构应该是开弦A模型量子上同调的一部分。我们得到的预测真正的Ooguri-Vafa不变量的拉格朗日膜上的五次P4，通过一些非平凡的一致性检查。本文讨论了Calabi-Yau四重上膜紧化对F-理论的提升以及由开闭形变空间的N=1特殊几何所决定的有效超引力作用量中的有效耦合。
We perform a Hodge theoretic study of parameter dependent families of D-branes on compact Calabi–Yau manifolds in type II and F-theory compactifications. Starting from a geometric Gauss–Manin connection for B-type branes we study the integrability and flatness conditions. The B-model geometry defines an interesting ring structure of operators. For the mirror A-model this indicates the existence of an open-string extension of the so-called A-model connection, whereas the discovered ring structure should be part of the open-string A-model quantum cohomology. We obtain predictions for genuine Ooguri–Vafa invariants for Lagrangian branes on the quintic in P4that pass some non-trivial consistency checks. We discuss the lift of the brane compactifications to F-theory on Calabi–Yau four-folds and the effective couplings in the effective supergravity action as determined by the N=1 special geometry of the open–closed deformation space.