<i>n</i> + 1 Dimensional Gravity Duals to Quantum Criticalities with Spontaneous Symmetry Breaking

Abstract

We reexamine the charged AdS domain wall solution to the Einstein-Abelian-Higgs model proposed by Gubser et al. as holographic superconductors at quantum critical points and comment on their statement about the uniqueness of gravity solutions. We generalize their explorations from 3 + 1 dimensions to arbitrary n + 1 Ds and find that the n + 1 ≥ 5D charged AdS domain walls are unstable against electric perturbations.