Infrared stability of ABJ-like theories

TL;DR

This work analyzes marginal and relevant deformations of ABJ/ABJM theories preserving $SU(2)_A \times SU(2)_B$ symmetry in three dimensions. Using two-loop perturbation theory, the authors derive beta-functions and show an IR-stable line of fixed points described by an ellipse in the $(y_1,y_2)$ plane, with the ABJ/ABJM point at $(y_1,y_2)=(0,2/K)$. Flavor couplings largely preserve IR stability, except when flavor sectors mix across gauge groups (the $\lambda_3$ direction), which can destabilize. For relevant deformations, no perturbatively accessible IR fixed points other than the free UV fixed point are found, aligning with the conjectured strongly coupled IR fixed point in the AdS$_4$/CFT$_3$ setup.

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].

Figures (4)

• Figure 1: Two--loop diagrams contributing to the anomalous dimensions of fundamental chiral superfields. Straight lines correspond to chirals, whereas wave lines to vectors.
• Figure 2: Line of fixed points and RG trajectories. The arrows indicate flows towards the IR. We have chosen $K=100$, $N=10$, $M=20$.
• Figure 3: The ellipse of fixed points in the $(\lambda_1,\lambda_2,\lambda_3)$ space for the flavored model with $\alpha_i=0$. The parameters are $K=100$, $M=N=50$, $N_f=N_f\prime=5$.
• Figure 4: RG trajectories for the flavored model with $\lambda_i=0$ and $\alpha_1=\alpha_2 \neq 0$. The arrows indicate flows towards the IR. We have chosen $K=100$, $M=N=50$, $N_f=N_f\prime=5$.