Holographic quantum critical points in Lifshitz space-time

Abstract

We study a minimally coupled charged scalar field in a charged Lifshitz back- ground. For z = 2, we find an analytic expression for the corresponding low energy retarded Green's function. Unlike the RN-AdS case, the position of the superfluid surfaces depends on the charge of the scalar field only through the IR scaling dimension. We show that by increasing the dynamical exponent, the dual theory becomes more stable. We also show that the background could suffer from an instability of the IR geometry leading to a bifur- cating critical point. It also allows the existence of scalar hair, causing hybridized critical point. We have investigated stable and unstable regions in the parameter space.