Holographic, N=1 Supersymmetric RG Flows on M2 Branes

TL;DR

This paper constructs and analyzes a family of holographic N=1 supersymmetric RG flows on M2 branes, revealing fixed points with G_2 and SU(3)xU(1) symmetry and providing insights into operator dimensions and supersymmetry constraints.

Contribution

The study introduces new holographic RG flow solutions with N=1 supersymmetry driven by two mass parameters, connecting G_2 and SU(3)xU(1) fixed points, and predicts operator anomalous dimensions.

Findings

Flow from G_2 to SU(3)xU(1) fixed point with N=1 supersymmetry.

Supergravity predicts anomalous dimension 1/√6 for flow-driving operators.

Limited field theory analysis due to insufficient protection by N=1 supersymmetry.

Abstract

We find a family of holographic N=1 supersymmetric RG flows on M2 branes. These flows are driven by two mass parameters from the maximally (N=8) supersymmetric theory and the infra-red theory is controlled by two fixed points, one with G_2 symmetry and the other with SU(3)xU(1) symmetry and N=2 supersymmetry. The generic flow, with unequal mass parameters, is N=1 supersymmetric but goes to the SU(3)xU(1) symmetric, N=2 supersymmetric fixed point, where the masses are equal. The only flow that goes to the G_2 symmetric point occurs when one of the mass parameters is set to zero. There is an N=1 supersymmetric flow from the G_2 symmetric point to the SU(3)xU(1) symmetric point and supergravity gives a prediction of 1/\sqrt{6} for the anomalous dimensions of the operators that drive this flow. We examine these flows from the field theory perspective but find that one is limited to qualitative results since N=1 supersymmetry in three dimensions is insufficient to protect the form and dimensions of the operators involved in the flow.