Analog systems for gravity duals

We show that analog gravity systems exist for charged, planar black holes in asymptotic anti-de Sitter space. These black holes have been employed to describe, via the gauge-gravity duality, strongly coupled condensed matter systems on the boundary of anti-de Sitter (AdS) space. The analog gravity system is a different condensed matter system that, in a suitable limit, describes the same bulk physics as the theory on the AdS boundary. This combination of the gauge-gravity duality and analog gravity therefore suggests a duality between different condensed matter systems.

Figure 1

Sketch of relations between different expressions of the same theory. Shown is the asymptotic coordinate, $z$, of AdS space and one of the perpendicular coordinates $x_1$. We will assume that we have a translational symmetry in the $x_1$ direction and will here only consider the static case, thus the time coordinate is not shown. The boundary of AdS space is at $z=0$, where we have a strongly coupled condensed matter system. The AdS/CMT correspondence relates this boundary theory to a gravitational theory in the bulk which contains fields propagating in the curved background. The same gravitational system can alternatively be described as an analog gravity system in which the metric in AdS space is only emergent for weakly coupled perturbations propagating in some fluid’s background. Projected onto a subspace, one now has two condensed matter systems in flat space-time of the same dimension that describe the same physics, if in entirely different ways. What is the relation between these two theories?