Holographic quantum critical points in Lifshitz space-time

TL;DR

This paper investigates holographic quantum critical points in Lifshitz space-time, deriving analytic Green's functions, analyzing stability, and exploring phase transitions related to scalar hair and IR instabilities.

Contribution

It provides an analytic expression for the Green's function in Lifshitz backgrounds and explores stability and phase transition phenomena unique to these geometries.

Findings

Analytic Green's function for z=2 Lifshitz background.

Stability increases with higher dynamical exponent z.

Identification of IR instabilities leading to bifurcating critical points.

Abstract

We study a minimally coupled charged scalar field in a charged Lifshitz background. 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 bifurcating critical point. It also allows the existence of scalar hair, causing hybridized critical point. We have investigated stable an unstable regions in the parameter space.