Collective dynamics and the Anderson-Higgs mechanism in a bona fide holographic superconductor

The holographic superconductor is one of the most popular models in context applied holography. Despite what its name suggests, it does not describe a superconductor. On contrary, low temperature phase dual field theory superfluid with spontaneously broken U(1) global symmetry. As already observed previous literature, bona fide can be constructed using mixed boundary conditions for bulk gauge field. By exploiting this prescription, we study near-equilibrium collective dynamics Higgs and reveal characteristic features Anderson-Higgs mechanism. We show that second sound disappears from spectrum acquires finite energy gap order plasma frequency. observe an overdamped to underdamped crossover mode which below $\approx T_c/2$, $T_c$ superconducting critical temperature. Interestingly, at significantly smaller than $2\Delta$, $\Delta$ gap. Finally, interpret our results Ginzburg-Landau confirm validity previously derived perturbative analytic expressions.