Gapped dilatons in scale invariant superfluids

TL;DR

This paper investigates a field theory model with spontaneously broken $U(1)$ and scale symmetries, revealing a light dilaton and a phonon mode with speed of sound, relevant for understanding conformal fluids and condensed matter systems.

Contribution

It demonstrates the mixing between the $U(1)$ Nambu-Goldstone mode and the dilaton, providing a detailed analysis of their dynamics and implications for superfluid behavior.

Findings

Identification of a light dilaton with a gap set by chemical potential

Discovery of mixing between Nambu-Goldstone mode and dilaton affecting phonon dynamics

Extension of results to boosted superfluids and condensed matter relevance

Abstract

We study a paradigmatic model in field theory where a global $U(1)$ and scale symmetries are jointly and spontaneously broken. At zero density the model has a non-compact flat direction, which at finite density needs to be slightly lifted. The resulting low-energy spectrum is composed by a standard gapless $U(1)$ Nambu-Goldstone mode and a light dilaton whose gap is determined by the chemical potential and corrected by the couplings. Even though $U(1)$ and scale symmetries commute, there is a mixing between the $U(1)$ Nambu-Goldstone and the dilaton that is crucial to recover the expected dynamics of a conformal fluid and leads to a phonon propagating at the speed of sound. The results rely solely on an accurate study of the Ward-Takahashi identities and are checked against standard fluctuation computations. We extend our results to a boosted superfluid, and comment the relevance of our findings to condensed matter applications.