A Holographic Superfluid Symphony

TL;DR

This paper investigates the hydrodynamic excitations of holographic superfluids by analyzing quasinormal modes and their support across the phase diagram, providing insights into the dispersion relations and sound modes.

Contribution

It introduces a comprehensive analysis of QNMs in holographic superfluids, including support in complex frequency and momentum, and clarifies the nature of sound modes beyond weak coupling approximations.

Findings

Rules out role-reversal between first and second sound

Reconstructs hydrodynamic dispersion relations from QNM support

Analyzes low-energy excitations beyond standard QNM picture

Abstract

We study the hydrodynamic excitations of backreacted holographic superfluids by computing the full set of quasinormal modes (QNMs) at finite momentum and matching them to the existing hydrodynamic theory of superfluids. Additionally, we analyze the behavior of the low-energy excitations in real frequency and complex momentum, going beyond the standard QNM picture. Finally, we carry out a novel type of study of the model by computing the support of the hydrodynamic modes across the phase diagram. We achieve this by determining the support of the corresponding QNMs on the different operators in the dual theory, both in complex frequency and complex momentum space. From the support, we are able to reconstruct the hydrodynamic dispersion relations using the hydrodynamic constitutive relations. Our analysis rules out a role-reversal phenomenon between first and second sound in this model, contrary to results obtained in a weakly coupled field theory framework.