Conductivity and entanglement entropy of high dimensional holographic superconductors

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We investigate the dependence of the conductivity and the entanglement entropy on the space-time dimensionality $d$ in two holographic superconductors: one dual to a quantum critical point with spontaneous symmetry breaking, and the other modeled by a charged scalar that condenses at a sufficiently low temperature in the presence of a Maxwell field.

• In both cases the gravity background is asymptotically Anti de Sitter (AdS).
• In the large $d$ limit we obtain explicit analytical results for the conductivity at zero temperature and the entanglement entropy by a $1/d$ expansion.
• We show that the entanglement entropy is always smaller in the broken phase.