Analog dual to a 2+1-dimensional holographic superconductor

TL;DR

This paper proposes an analog gravity model based on fluid dynamics that mimics a 3+1-dimensional AdS spacetime dual to a 2+1-dimensional superconductor, enabling potential experimental realization.

Contribution

It introduces a hydrodynamic analog model that replicates the AdS$_4$ bulk and its holographic dual, including the metric and entanglement entropy calculations.

Findings

The analog model reproduces the AdS$_4$ metric in fluid dynamics.

Entanglement entropy can be computed in the analog system.

The model suggests possible experimental realization of holographic superconductor features.

Abstract

We study an analog hydrodynamic model that mimics a 3+1 AdS planar BH spacetime dual to a 2+1-dimensional superconductor. We demonstrate that the AdS$_4$ bulk and its holographic dual could be realized in nature in an analog gravity model based on fluid dynamics. In particular we mimic the metric of an $O_2$ holographic superconductor and calculate the entanglement entropy of a conveniently designed subsystem at the boundary of the analog AdS$_4$ bulk.