Holographic Zero Sound from Spacetime-Filling Branes

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.

v2: minor corrections and edits, no changes to results, version published in JHEP

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• Adding new branches to the "Christmas tree" of the quasinormal spectrum of black branes
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• Holographic Response of Electron Clouds
• Density response of holographic metallic IR fixed points with translational pseudo-spontaneous symmetry breaking
• Zero sound and higher-form symmetries in compressible holographic phases
• Holographic fundamental matter in multilayered media
• Quasinormal Modes and Correlators in the Shear Channel of Spacetime-Filling Branes
• Transport properties of DBI action
• Entanglement and Excitations in Gauge/Gravity Duality