Conductivity and entanglement entropy of high dimensional holographic superconductors

TL;DR

This paper explores how conductivity and entanglement entropy in high-dimensional holographic superconductors depend on spacetime dimensionality, revealing that higher dimensions weaken condensate interactions and alter physical properties.

Contribution

It provides explicit analytical results for conductivity and entanglement entropy in high dimensions using a $1/d$ expansion, highlighting the effects of increasing dimensionality.

Findings

Entanglement entropy decreases with higher dimensions.

The coherence peak in conductivity narrows as dimension increases.

The ratio of energy gap to critical temperature decreases in high dimensions.

Abstract

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.