Stability analysis of holographic RG flows in 3d supergravity

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.

Automated summary

In this study, we investigate holographic RG flows in a 3d supergravity model using the methods of dynamical system theory. By reducing the gravity equations of motion to an autonomous dynamical system, we identify equilibrium points and analyze their stability. We also reconstruct asymptotic solutions near critical points, which consist of two types: asymptotically AdS metrics and hyperscaling violating metrics. Furthermore, we describe possible RG flows between an unstable (saddle) UV fixed point and a stable (stable node) IR fixed point, as well as analyze bifurcations in the model.