Criteria For Superfluid Instabilities of Geometries with Hyperscaling Violation

TL;DR

This paper derives analytical criteria for superfluid instabilities in geometries with hyperscaling violation and Lifshitz scaling, highlighting the role of scalar couplings and minimal charge requirements.

Contribution

It provides the first analytical conditions for superfluid instabilities in hyperscaling-violating geometries, including the effects of scalar couplings and charge thresholds.

Findings

Analytical criteria for scalar instabilities at zero temperature.

Conditions under which a minimal charge triggers superfluid transition.

Numerical examples illustrating finite temperature effects.

Abstract

We examine the onset of superfluid instabilities for geometries that exhibit hyperscaling violation and Lifshitz-like scaling at infrared and intermediate energy scales, and approach AdS in the ultraviolet. In particular, we are interested in the role of a non-trivial coupling between the neutral scalar supporting the scaling regime, and the (charged) complex scalar which condenses. The analysis focuses exclusively on unstable modes arising from the hyperscaling-violating portion of the geometry. Working at zero temperature, we identify simple analytical criteria for the presence of scalar instabilities, and discuss under which conditions a minimal charge will be needed to trigger a transition. Finite temperature examples are constructed numerically for a few illustrative cases.