Inverse problem of correlation functions in holography and bulk reconstruction

Abstract: This paper shows that the exterior of a planar/spherically/hyperbolically symmetric asymptotically anti-de Sitter static black brane/hole can be reconstructed from its boundary frequency 2-point correlation functions of arbitrary two probe scalar operators by solving a Gel'fand-Levitan-Marchenko integral equation. A method about how to solve this integral equation is also presented. Since the frequency correlation function is easily handled in experiments and theories, this paper not only proposes an explicit method to "directly measure" the corresponding holographic spacetime for a material that has holographic dual but also provides a powerful approach to experimentally check if a system has holographic dual.