D-膜的A-型，他们的变形，和Morse协边的A-膜上的Calabi-Yau 3-folds在分裂吸引流：唐纳森/亚历山大-希尔登-洛萨诺-蒙特西诺斯-瑟斯顿/赫维茨/德尼夫-乔伊斯会议Polchinski-Grothendieck
D-branes of A-type, their deformations, and Morse cobordism of A-branes on Calabi-Yau 3-folds under a split attractor flow: Donaldson/Alexander-Hilden-Lozano-Montesinos-Thurston/Hurwitz/Denef-Joyce meeting Polchinski-Grothendieck
摘要：
在[L-Y 5]（D（6）：arXiv：1003.1178 [math.SG]）中，我们引入了Azumaya $C^{\infty}$ -流形的概念，该流形具有一个基本模和从其到一个复流形的态射。在当前的续集中，我们使用这个概念给出了A型超对称D膜（即A膜）的原型定义-在威尔逊理论的弦理论空间的适当区域-作为特殊的拉格朗日态射，这些对象具有酉的，极小平坦的连接与奇点。这合并唐纳森的图片特殊拉格朗日子流形和Polchinski-Grothendieck Anglands的D膜上的卡-丘空间。D-膜的基本现象，如希格斯辛/非希格斯辛和大膜与小膜包裹，可以通过这种态射的变形来实现。亚历山大、希尔登、洛扎诺、蒙特西诺斯和瑟斯顿的经典结果则暗示了D3-膜的路径积分的类亏格展开。D2-膜和M2-膜也是如此。在最后一节中，我们使用乔伊斯关于特殊的具有圆锥奇点的拉格朗日子流形的去奇异化的技术结果来解释A-膜如何在分裂吸引子流下被驱动和重新组装，正如Denef早期的工作所研究的那样。本节将与Denef的arXiv：hep-th/0107152和Joyce的arXiv：math.DG/0303272一起阅读。
英文摘要：
In [L-Y5] (D(6): arXiv:1003.1178 [math.SG]) we introduced the notion of Azumaya $C^{\infty}$-manifolds with a fundamental module and morphisms therefrom to a complex manifold. In the current sequel, we use this notion to give a prototypical definition of supersymmetric D-branes of A-type (i.e. A-branes) -- in an appropriate region of the Wilson's theory-space of string theory -- as special Lagrangian morphisms from such objects with a unitary, minimally flat connection-with-singularities. This merges Donaldson's picture of special Lagrangian submanifolds and the Polchinski-Grothendieck Ansatz for D-branes on a Calabi-Yau space. Basic phenomena of D-branes such as Higgsing/un-Higgsing and large- vs. small-brane wrapping can be realized via deformations of such morphisms. Classical results of Alexander, Hilden, Lozano, Montesinos, and Thurston suggest then a genus-like expansion of the path-integral of D3-branes. Similarly for D2-branes and M2-branes. In the last section, we use the technical results of Joyce on desingularizations of special Lagrangian submanifolds with conical singularities to explain how A-branes thus defined can be driven and re-assemble under a split attractor flow, as studied in an earlier work of Denef. This section is to be read with arXiv:hep-th/0107152 of Denef and arXiv:math.DG/0303272 of Joyce.
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