Renormalization group flows in $3d$ holographic model

In the context of AdS/CFT correspondence, we study renormalization group flows in $3d$ supergravity with a scalar field (dilaton) and its potential. Using the dynamical systems theory, the stationary points of the corresponding equations of motion are analyzed for stability. Asymptotic solutions for the metric and the scalar field are restored in their vicinity. We show that some solutions can be interpreted as the fixed points of the dual field theory and that there are RG flows between an unstable UV fixed point and a stable IR fixed point.