Conductivity and entanglement entropy of high dimensional holographic superconductors

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. As dimensionality increases, the entanglement entropy decreases, the coherence peak in the conductivity becomes narrower and the ratio between the energy gap and the critical temperature decreases. These results suggest that the condensate interactions become weaker in high spatial dimensions.Comment: 38 pages, 7 figure

Coherence effects in disordered geometries with a field-theory dual

We investigate the holographic dual of a probe scalar in an asymptotically Anti-de-Sitter (AdS) disordered background which is an exact solution of Einstein's equations in three bulk dimensions. Unlike other approaches to model disorder in holography, we are able to explore quantum wave-like interference effects between an oscillating or random source and the geometry. In the weak-disorder limit, we compute analytically and numerically the one-point correlation function of the dual field theory for different choices of sources and backgrounds. The most interesting feature is the suppression of the one-point function in the presence of an oscillating source and weak random background. We have also computed analytically and numerically the two-point function in the weak disorder limit. We have found that, in general, the perturbative contribution induces an additional power-law decay whose exponent depends on the distribution of disorder. For certain choices of the gravity background, this contribution becomes dominant for large separations which indicates breaking of perturbation theory and the possible existence of a phase transition induced by disorder.Comment: 36 pages, 19 figs, v3 accepted versio