Resolving Lifshitz Horizons

TL;DR

This paper investigates the Lifshitz horizons in holographic models, showing that generic corrections replace the Lifshitz geometry with a regular $AdS_2 imes R^2$ space, resolving mild singularities.

Contribution

It demonstrates that in Einstein-Maxwell-dilaton theories, Lifshitz geometries are replaced by $AdS_2 imes R^2$ in the IR due to generic corrections, curing singularities.

Findings

Lifshitz horizons exhibit mild singularities with diverging tidal forces.

Generic corrections lead to a transition from Lifshitz to $AdS_2 imes R^2$ geometry.

The Lifshitz scaling persists over a wide energy range before being replaced.

Abstract

Via the AdS/CFT correspondence, ground states of field theories at finite charge density are mapped to extremal black brane solutions. Studies of simple gravity + matter systems in this context have uncovered wide new classes of extremal geometries. The Lifshitz metrics characterising field theories with non-trivial dynamical critical exponent $z \neq 1$ emerge as one common endpoint in doped holographic toy models. However, the Lifshitz horizon exhibits mildly singular behaviour - while curvature invariants are finite, there are diverging tidal forces. Here we show that in some of the simplest contexts where Lifshitz metrics emerge, Einstein-Maxwell-dilaton theories, generic corrections lead to a replacement of the Lifshitz metric, in the deep infrared, by a re-emergent $AdS_2 \times R^2$ geometry. Thus, at least in these cases, the Lifshitz scaling characterises the physics over a wide range of energy scales, but the mild singularity is cured by quantum or stringy effects.