Infrared Stability of N=2 Chern-Simons Matter Theories

TL;DR

This paper investigates the infrared stability of N=2 supersymmetric Chern-Simons matter theories using two-loop RG flow analysis, revealing complex fixed point structures and conditions for conformal invariance.

Contribution

It provides a comprehensive two-loop analysis of fixed points and their stability in N=2 Chern-Simons matter theories, including models with flavors and deformations.

Findings

Identification of globally IR stable fixed points with a single stability direction.

Discovery of fixed point surfaces with local instability in certain models.

Conditions under which beta-functions vanish but theories are not finite.

Abstract

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.