Universal scaling properties of extremal cohesive holographic phases

TL;DR

This paper classifies strongly-coupled holographic IR phases at finite density based on metric and field scaling, revealing how critical exponents influence stability, conductivity, and entanglement properties, regardless of specific model details.

Contribution

It introduces a universal classification scheme for holographic phases using four critical exponents, applicable to both relativistic and non-relativistic cases, and links these exponents to physical properties.

Findings

Classification into two phase classes based on symmetry breaking.

Critical exponents determine stability and low-frequency conductivity.

Deviation from Ryu-Takayanagi surface scaling characterized by exponents.

Abstract

We show that strongly-coupled, translation-invariant holographic IR phases at finite density can be classified according to the scaling behaviour of the metric, the electric potential and the electric flux introducing four critical exponents, independently of the details of the setup. Solutions fall into two classes, depending on whether they break relativistic symmetry or not. The critical exponents determine key properties of these phases, like thermodynamic stability, the (ir)relevant deformations around them, the low-frequency scaling of the optical conductivity and the nature of the spectrum for electric perturbations. We also study the scaling behaviour of the electric flux through bulk minimal surfaces using the Hartnoll-Radicevic order parameter, and characterize the deviation from the Ryu-Takayanagi prescription in terms of the critical exponents.