Renormalization Group Flows from D=3, N=2 Matter Coupled Gauged Supergravities

Abstract

We study holographic RG flows of N=2 matter couple AdS_3 supergravities which admit both compact and non-compact sigma manifolds. For the compact case the supersymmetric domain wall solution interpolates between a conformal IR region and flat spacetime and this corresponds to a deformation of the CFT by an irrelevant operator. When it is non-compact, the solution can be interpreted as a flow between an UV fixed point and a non-conformal(singular) IR region. This is an exact example of a deformation flow when the singularity is physical. We also find a non-supersymmetric deformation flow when the scalar potential has a second AdS vacua. The ratio of the central charges is rational for certain values of the size of the sigma model. Next, we analyze the spectrum of a massless scalar on our background by transforming the problem into Schroedinger form. The spectrum is continuous for the compact model, yet it can be both continuous (with or without mass gap) and discrete otherwise. Finally, 2-point functions are computed for two examples whose quantum mechanical potentials are of Calogero type.