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

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

Automated summary

The holographic superconductor is a popular model in applied holography. It describes a superfluid phase with a spontaneously broken U(1) global symmetry rather than a superconductor. By using mixed boundary conditions, a genuine holographic superconductor can be constructed, and its near-equilibrium dynamics in the Higgs phase and the characteristic features of the Anderson-Higgs mechanism can be studied. The results show the disappearance of second sound and the emergence of a finite energy gap for the gauge field.