From Weak to Strong Coupling in ABJM Theory
From Weak to Strong Coupling in ABJM Theory
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DOI：
10.1007/s00220-011-1253-6
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发表时间：
2010-07
影响因子：
2.4
通讯作者：
N. Drukker;M. Mariño;Pavel Putrov
中科院分区：
文献类型：
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作者：
N. Drukker;M. Mariño;Pavel Putrov
超对称Chern-Simons物质理论（简称ABJM理论）的配分函数以及Wilson环的某些可观测量都可以用一个零维超矩阵模型来描述。这个超矩阵模型与描述透镜空间上拓扑Chern-Simons理论的矩阵模型密切相关。我们进一步探讨这些最近的观察，并提取更准确的结果在ABJM理论的矩阵模型。特别是，我们计算的平面自由能，它匹配在强耦合的经典IIA超引力作用，并给出了正确的N3/2标度的自由度的M2膜理论的数量。此外，我们发现贡献来自世界片瞬子修正。我们还计算了非平面修正，自由能和威尔逊回路的期望值。这个矩阵模型也出现在复曲面卡-丘流形上拓扑弦的研究中，并且在平面ABJM理论的耦合空间和这个卡-丘流形的模空间之间产生了一种有趣的联系。特别是它表明，除了通常的微扰和强耦合（AdS）的扩展，第三个自然的扩展轨迹是两个't Hooft耦合消失，另一个是有限的线。这是卡-丘的圆锥形轨迹，并导致围绕拓扑陈-西蒙斯理论的扩展。我们提出了一些明确的结果的配分函数和威尔逊环的观测量在这个轨迹。
The partition function ofsupersymmetric Chern–Simons-matter theory (known as ABJM theory) on, as well as certain Wilson loop observables, are captured by a zero dimensional super-matrix model. This super–matrix model is closely related to a matrix model describing topological Chern–Simons theory on a lens space. We explore further these recent observations and extract more exact results in ABJM theory from the matrix model. In particular we calculate the planar free energy, which matches at strong coupling the classical IIA supergravity action onand gives the correctN3/2scaling for the number of degrees of freedom of the M2 brane theory. Furthermore we find contributions coming from world-sheet instanton corrections in. We also calculate non-planar corrections, both to the free energy and to the Wilson loop expectation values. This matrix model appears also in the study of topological strings on a toric Calabi–Yau manifold, and an intriguing connection arises between the space of couplings of the planar ABJM theory and the moduli space of this Calabi–Yau. In particular it suggests that, in addition to the usual perturbative and strong coupling (AdS) expansions, a third natural expansion locus is the line where one of the two ’t Hooft couplings vanishes and the other is finite. This is the conifold locus of the Calabi–Yau, and leads to an expansion around topological Chern–Simons theory. We present some explicit results for the partition function and Wilson loop observables around this locus.