Stability analysis of holographic RG flows in 3d supergravity

TL;DR

This paper analyzes the stability and bifurcations of holographic RG flows in a 3d supergravity model by reducing the equations to a dynamical system and studying equilibrium points.

Contribution

It introduces a dynamical systems approach to holographic RG flows in 3d supergravity, identifying fixed points and their stability, and classifying possible flow solutions.

Findings

Identified equilibrium points with AdS and hyperscaling violating metrics.

Classified RG flows between UV and IR fixed points.

Analyzed bifurcations in the dynamical system.

Abstract

We study holographic RG flows in a 3d supergravity model from the side of the dynamical system theory. The gravity equations of motion are reduced to an autonomous dynamical system. Then we find equilibrium points of the system and analyze them for stability. We also restore asymptotic solutions near the critical points. We find two types of solutions: with asymptotically AdS metrics and hyperscaling violating metrics. We write down possible RG flows between an unstable (saddle) UV fixed point and a stable (stable node) IR fixed point. We also analyze bifurcations in the model.