非相对论性ABJM理论中的观测量和关联函数
Observables and Correlators in Nonrelativistic ABJM Theory
摘要：
非相对论ABJM理论是由伽利略质量极限-形变N=6的Chern-Simons理论定义的。全息弦论的对偶理论还不为人所知。为了理解候选引力对偶可能表现出的特征，我们研究了非相对论ABJM理论中的局部和非局部物理观测量及其相关性。我们表明，规范不变的局部可观量对应于零范数状态，它们之间的关联函数是平凡的。我们还表明，一类特殊的非局部观测量，威尔逊圈，拓扑意义上说，他们的关联函数与纯陈-西蒙斯理论相一致。我们认为，该理论仍然是物理和说明几个物理观测值的关联函数是非平凡的。我们还研究量子方面。我们证明了Chern-Simons能级是重正化的，作用在自旋链上的伸缩算符在平面极限下是平凡的。这些结果都指向引力对偶的弦尺度几何和在其上定义的对偶弦的有趣的拓扑和无张力性质。
英文摘要：
Non-relativistic ABJM theory is defined by Galilean limit of mass-deformed N=6 Chern-Simons theory. Holographic string theory dual to the theory is not known yet. To understand features candidate gravity dual might exhibit, we examine local and nonlocal physical observables and their correlations in the non-relativistic ABJM theory. We show that gauge invariant local observables correspond to zero-norm states and that correlation functions among them are trivial. We also show that a particular class of nonlocal observables, Wilson loops, are topological in the sense that their correlation functions coincide with those of pure Chern-Simons theory. We argue that the theory is nevertheless physical and illustrate several physical observables whose correlation functions are nontrivial. We also study quantum aspects. We show that Chern-Simons level is finitely renormalized and that dilatation operator acting on spin chain is trivial at planar limit. These results all point to string scale geometry of gravity dual and to intriguing topological and tensionless nature of dual string defined on it.
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