Gapped dilatons in scale invariant superfluids
arXiv:2006.11047 · doi:10.1103/PhysRevD.102.076011
Abstract
We study a paradigmatic model in field theory where a global 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 Nambu-Goldstone mode and a light dilaton whose gap is determined by the chemical potential and corrected by the couplings. Even though and scale symmetries commute, there is a mixing between the 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.
22 pages. v2: references added. v3: version to appear in journal
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