Order parameter fluctuations in the holographic superconductor

We investigate the effect of order parameter fluctuations in the holographic superconductor. In particular, using a fully backreacted bulk geometry, the intrinsic spectral functions of the order parameter in both the normal and the superconducting phase are computed. We also present a vector-like large-$N$ version of the Ginzburg-Landau model that accurately describes our long-wavelength results in both phases. The large-$N$ limit of the latter model explains why the Higgs mode and the second-sound mode are not present in the spectral functions. Our results indicate that the holographic superconductor describes a relativistic multi-component superfluid in the universal regime of the BEC-BCS crossover.