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

Abstract

Abstract 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 ≈ Tc/2, with Tc the superconducting critical temperature. Interestingly, the energy gap of the Higgs mode at low temperature is significantly smaller than 2∆, with ∆ the superconducting energy gap. Finally, we interpret our results using Ginzburg-Landau theory and we confirm the validity of previously derived perturbative analytic expressions.