Nearly Critical Holographic Superfluids

TL;DR

This paper investigates the near-critical behavior of holographic superfluids at finite temperature and chemical potential, deriving an effective theory for long-wavelength modes and analyzing their dispersion relations.

Contribution

It introduces an analytic effective theory for holographic superfluids near criticality, matching it with Model F and computing dissipative transport coefficients from black hole data.

Findings

Dispersion relations are discontinuous between phases at finite density.

Derived an effective long-wavelength theory for gapless modes.

Computed kinetic transport coefficients from thermodynamics and horizon data.

Abstract

We study the nearly critical behaviour of holographic superfluids at finite temperature and chemical potential in their probe limit. This allows us to examine the coupled dynamics of the full complex order parameter with the charge density of the system. We derive an effective theory for the long wavelength limit of the gapless and pseudo-gapped modes by using analytic techniques in the bulk. We match our construction with Model F in the classification of Hohenberg and Halperin and compute the complex dissipative kinetic transport coefficient in terms of thermodynamics and black hole horizon data. We carry out an analysis of the corresponding modes and argue that at finite density the dispersion relations are discontinuous between the normal and the broken phase. We compare and contrast our results with earlier numerical work.