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arXiv 0912.4282hep-th
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N=2的Chern-Simons物质理论的红外稳定性

Infrared Stability of N=2 Chern-Simons Matter Theories

Marco S. Bianchi, Silvia Penati, Massimo Siani

摘要:

根据AdS 4/CFT 3对应,N=2超对称Chern-Simons物质理论在红外波段应该有一个稳定的不动点.为了支持这一预测,我们研究RG流的二能级陈-西蒙斯物质理论与/没有味道引起的最一般的边缘超势兼容N=2超对称性。在两个环路上,我们确定了不动点的完整光谱,并研究了它们的红外稳定性。我们的分析涵盖了一个大类的模型,包括扰动的ABJM/ABJ理论和没有味道,N= 2,3理论与不同的CS水平对应于打开罗马人的质量和β变形。在所有的情况下,我们发现曲线(或表面)的不动点是全球IR稳定,但局部不稳定在以下意义上:该系统只有一个方向的稳定性,在ABJM的情况下,符合最大的全球对称性保持扰动,而沿任何其他方向,它流到一个不同的不动点的表面上。共形不变性与有限性的问题也得到了解决:虽然在一般情况下,消失的beta函数意味着两个循环的有限性,我们发现一组特殊的调味理论,这不再是真的。

英文摘要:

According to the AdS4/CFT3 correspondence, N=2 supersymmetric Chern-Simons matter theories should have a stable fixed point in the infrared. In order to support this prediction we study RG flows of two-level Chern-Simons matter theories with/without flavors induced by the most general marginal superpotential compatible with N=2 supersymmetry. At two loops we determine the complete spectrum of fixed points and study their IR stability. Our analysis covers a large class of models including perturbations of the ABJM/ABJ theories with and without flavors, N=2,3 theories with different CS levels corresponding to turning on a Romans mass and beta-deformations. In all cases we find curves (or surfaces) of fixed points which are globally IR stable but locally unstable in the following sense: The system has only one direction of stability which in the ABJM case coincides with the maximal global symmetry preserving perturbation, whereas along any other direction it flows to a different fixed point on the surface. The question of conformal invariance vs. finiteness is also addressed: While in general vanishing beta-functions imply two-loop finiteness, we find a particular set of flavored theories where this is no longer true.

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