Holographic zero sound from spacetime-filling branes

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 nonlinearity 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 nonlinearity parameter where two other proposed de finitions of the crossover are viable, via pole collisions in Green's functions or peak movement in the charge density spectral function.