Aspects of Current Correlators in Holographic Theories with Hyperscaling Violation

TL;DR

This paper investigates the behavior of current correlators in holographic theories with hyperscaling violation, identifying conditions for stable low-energy excitations resembling zero sound and exploring their physical interpretations.

Contribution

It provides a detailed analysis of low-energy excitations in holographic theories with hyperscaling violation, highlighting the presence or absence of zero sound-like modes under various conditions.

Findings

Stable linearly-dispersing mode exists for certain z and θ values.

The mode resembles zero sound in Fermi liquids.

Theories with θ = d-1 do not exhibit zero sound-like modes.

Abstract

We study the low energy and low momentum behavior of current correlators in a class of holographic zero-temperature finite density critical theories which do not respect the hyperscaling relation. The dual holographic description is assumed to be given by probe D-branes embedded in background geometries characterized by a dynamical critical exponent $z$ and a hyperscaling violation exponent $\theta$. We show that a subset of these theories with $1\leq z<2(1-\theta/d)$ exhibit a stable linearly-dispersing mode in their low energy spectrum of excitations. This mode, which appears as a pole in the retarded correlators of charge density and longitudinal currents, has some characteristics similar to that of the zero sound in Fermi liquids. Given some reasonable assumptions, we argue that the class of theories with $\theta =d-1$ that logarithmically violate the area law in the entanglement entropy in a manner reminiscent of theories with Fermi surfaces, does \emph {not} exhibit a zero sound-like mode in the low energy spectrum of the probe sector. Furthermore, utilizing the holographic Wilsonian approach, we explicitly show that such a mode has a natural interpretation as a Goldston boson arising from the spontaneous breaking of a specific symmetry.