Holographic Zero Sound from Spacetime-Filling Branes

TL;DR

This paper uses holography to analyze zero sound modes in strongly-interacting conformal field theories with finite temperature and chemical potential, revealing Fermi-liquid-like behavior and crossover phenomena through gravitational dual models.

Contribution

It demonstrates the existence of zero sound in holographic models with spacetime-filling branes across various parameters, extending the understanding of collective modes beyond traditional hydrodynamics.

Findings

Zero sound exists at low T/μ outside hydrodynamic regime.

Sound attenuation resembles Fermi liquid behavior with a maximum.

Identifies crossover regimes via pole collisions and spectral function analysis.

Abstract

We use holography to study sound modes of strongly-interacting conformal field theories with non-zero temperature, $T$, and $U(1)$ chemical potential, $\mu$. Specifically, we consider charged black brane solutions of Einstein gravity in $(3+1)$-dimensional Anti-de Sitter space coupled to a $U(1)$ gauge field with Dirac-Born-Infeld action, representing a spacetime-filling brane. The brane action has two free parameters: the tension and the non-linearity parameter, which controls higher-order terms in the field strength. For all values of the tension, non-linearity parameter, and $T/\mu$, and at sufficiently small momentum, we find sound modes with speed given by the conformal value and attenuation constant of hydrodynamic form. In particular we find sound at arbitrarily low $T/\mu$, outside the usual hydrodynamic regime, but in the regime where a Fermi liquid exhibits Landau's "zero" sound. In fact, the sound attenuation constant as a function of $T/\mu$ qualitatively resembles that of a Fermi liquid, including a maximum, which in a Fermi liquid signals the collisionless to hydrodynamic crossover. We also explore regimes of the tension and non-linearity parameter where two other proposed definitions of the crossover are viable, via pole collisions in Green's functions or peak movement in the charge density spectral function.