Fourth sound of holographic superfluids

TL;DR

This paper calculates the fourth sound in holographic superfluids, revealing how it approaches first sound at low temperatures for large scaling dimensions and exhibits non-conformal behavior for small ones, with potential to restore conformality.

Contribution

It demonstrates how the fourth sound behaves in holographic superfluids with different condensate scaling dimensions and introduces a scalar potential to enforce conformal invariance at low temperatures.

Findings

Fourth sound approaches first sound at low temperatures for large scaling dimensions.

Non-conformal behavior observed at low temperatures for small scaling dimensions.

Scalar potential can restore conformal invariance in the superfluid model.

Abstract

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.