  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.
