First Sound in Holographic Superfluids at Zero Temperature

TL;DR

This paper provides an analytical proof within the AdS/CFT framework that the gravity dual of an s-wave superfluid at zero temperature exhibits first sound, deriving the phonon dispersion relation in various dimensions.

Contribution

It offers the first analytical derivation of the superfluid phonon quadratic action and dispersion relation in holographic superfluids at zero temperature, extending previous numerical results.

Findings

Analytical derivation of the quadratic action for superfluid phonons.

Explicit expression for the dispersion relation of first sound.

Applicability to arbitrary dimensions and scalar potentials.

Abstract

Within the context of AdS/CFT, the gravity dual of an s-wave superfluid is given by scalar QED on an asymptotically AdS spacetime. While this conclusion is vastly supported by numerical arguments, here we provide an analytical proof that this is indeed the case. Working at zero temperature, we explicitly find the quadratic action for the superfluid phonon at the boundary in an arbitrary number of dimensions and for an arbitrary scalar field potential, recovering the known dispersion relation for conformal first sound.