Critical dynamics of holographic superfluids

A bstract We study the nearly critical behaviour of holographic superfluids at finite temperature and chemical potential. Using analytic techniques in the bulk, we derive an effective theory for the long wavelength dynamics of gapless and pseudo-gapped modes, at first subleading order in a derivative expansion and we match the classical limit of our field theory construction in a companion paper. Specifically, we obtain the constitutive relations for the stress tensor and electric current, as well as a time evolution equation for the order parameter at next-to-leading order. In addition, we get explicit formulas for all the transport coefficients in terms of background quantities. We carry out numerical cross-checks with the predictions of our effective theory close to the critical point.