Spacetime-emergent ring toward tabletop quantum gravity experiments

Abstract

We propose a way to discover, in tabletop experiments, spacetime-emergent materials, that is, materials holographically dual to higher-dimensional quantum gravity systems under the AdS/CFT. The emergence of the holographic spacetime is verified by a mathematical imaging transform of the response function on the material. We consider theories on a one-dimensional ring-shaped material and compute the response to a scalar source locally put at a point on the ring. When the theory on the material has a gravity dual, the imaging in the low-temperature phase exhibits a distinct difference from the ordinary materials: The spacetime-emergent material can look into the holographically emergent higher-dimensional curved spacetime and provides an image as if a wave had propagated there. Therefore the image is an experimental signature of the spacetime emergence. We also estimate the temperature, ring size, and source frequency usable in experiments, with an example of a quantum critical material, ${\mathrm{TlCuCl}}_{3}$.