arXiv 0905.34152009-05-21hep-th

M2理论的一个严格起源

A Stringy Origin of M2 Brane Chern-Simons Theories

Mina Aganagic

备注：: 39 pages, 3 figures
发表信息：: Nucl.Phys.B835:1-28,2010
DOI：: 10.1016/j.nuclphysb.2010.01.007

摘要：

我们证明了弦对偶把局部Calabi-Yau四重奇点X4上的M理论与实直线上的Calabi-Yau三重奇点X3上的IIA型弦论联系起来，RR 2-形式通量打开，RR通量编码了M理论圆如何在IIA几何上纤维化。关于探测X3的N个D2膜的理论是著名的三维N=2超对称性理论。我们发现，打开通量，并在横向的方向上的X3，对应于打开N=2陈-西蒙斯耦合。弦对偶意味着，在强耦合极限下，在这个背景下，X3上的N个D2膜变成了X4上的N个M2膜。这为最近用N=2的Chern-Simons理论描述Calabi-Yau四重上的M2膜理论提供了一个弦论推导。我们还提出了一个新的N=2的Chern-Simons理论，它是AdS_4 × Q^{1，1，1}的对偶. IIA型/M-理论对偶也将X3上的IIA弦论（只开启RR通量）与G2完整流形上的M-理论联系起来。我们表明，这意味着N M2膜探测的G2流形所描述的陈-西蒙斯理论起源于D2膜探测X3，除了现在陈-西蒙斯条款只保留N=1的超对称性在三维。

英文摘要：

We show that string duality relates M-theory on a local Calabi-Yau fourfold singularity X4 to type IIA string theory on a Calabi-Yau threefold X3 fibered over a real line, with RR 2-form fluxes turned on. The RR flux encodes how the M-theory circle is fibered over the IIA geometry. The theories on N D2 branes probing X3 are the well-known quiver theories with N=2 supersymmetry in three dimensions. We show that turning on fluxes, and fibering the X3 over a direction transverse to the branes, corresponds to turning on N=2 Chern-Simons couplings. String duality implies that, in the strong coupling limit, the N D2 branes on X3 in this background become N M2 branes on X4. This provides a string theory derivation for the recently conjectured description of the M2 brane theories on Calabi-Yau fourfolds in terms of N=2 quiver Chern-Simons theories. We also provide a new N=2 Chern-Simons theory dual to AdS_4 x Q^{1,1,1}. Type IIA/M-theory duality also relates IIA string theory on X3 with only the RR fluxes turned on, to M-theory on a G2 holonomy manifold. We show that this implies that the N M2 branes probing the G2 manifold are described by the quiver Chern-Simons theory originating from the D2 branes probing X3, except that now Chern-Simons terms preserve only N=1 supersymmetry in three dimensions.

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