Infrared stability of ABJ-like theories

TL;DR

This paper analyzes the infrared stability of ABJ-like theories with N=2 supersymmetry, identifying a stable line of fixed points and examining effects of marginal and relevant deformations, including flavor contributions.

Contribution

It provides a perturbative analysis of fixed points and their stability in ABJ-like theories, revealing a stable line of IR fixed points and effects of flavor and symmetry-breaking deformations.

Findings

A closed line of IR stable fixed points was found.

The ABJM/ABJ fixed point remains stable under SU(2)xSU(2) preserving deformations.

Flavor marginal superpotentials generally do not destabilize the IR fixed point.

Abstract

We consider marginal deformations of the superconformal ABJM/ABJ models which preserve N=2 supersymmetry. We determine perturbatively the spectrum of fixed points and study their infrared stability. We find a closed line of fixed points which is IR stable. The fixed point corresponding to the ABJM/ABJ models is stable under marginal deformations which respect the original SU(2)xSU(2) invariance, while deformations which break this group destabilize the theory which then flows to a less symmetric fixed point. We discuss the addition of flavor degrees of freedom. We prove that in general a flavor marginal superpotential does not destabilize the system in the IR. An exception is represented by a marginal coupling which mixes matter charged under different gauge sectors. Finally, we consider the case of relevant deformations which should drive the system to a strongly coupled IR fixed point recently investigated in arXiv:0909.2036 [hep-th].