Infrared stability of N=2 Chern-Simons matter theories

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. Each fixed point has only one direction of stability which in the ABJM case coincides with the maximal global symmetry preserving perturbation, whereas along any other direction the system flows to a different fixed point on the surface. The motion within the surface is driven by perturbations which are exactly marginal. 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.