Fourth sound of holographic superfluids

Understand

We compute fourth sound for superfluids dual to a charged scalar and a gauge field in an AdS_4 background.

• For holographic superfluids with condensates that have a large scaling dimension (greater than approximately two), we find that fourth sound approaches first sound at low temperatures.
• For condensates that a have a small scaling dimension it exhibits non-conformal behavior at low temperatures which may be tied to the non-conformal behavior of the order parameter of the superfluid.
• We show that by introducing an appropriate scalar potential, conformal invariance can be enforced at low temperatures.