  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.
