Emergent metric from wavelet-transformed quantum field theory

Abstract

We introduce a method of reverse holography by which a bulk metric is shown to arise from locally computable multiscale correlations of a boundary quantum field theory (QFT). The metric is obtained from the Petz-R\'enyi mutual information defined with input correlations computed from the continuous wavelet transform. The method is applicable to a variety of boundary QFTs that need not be conformal field theories (CFTs). For thermal free scalar and Dirac field theories the resulting bulk metric is that of (asymmetrically) warped anti-de Sitter (AdS) space. For massless, ground state CFTs the geometry simply reduces to AdS space. We show that certain parameters of the geometry can be tuned by changing the shape of the wavelet function.