Emergent metrics from wavelet-transformed quantum field theory

We propose a scheme by which a wavelet bulk description of a quantum field theory (QFT) can be equipped with a metric based on local multiscale correlation functions. The metric is obtained from the infinitesimal behaviour of the Petz-Rényi mutual information, which is computed from correlations that have been transformed with the continuous wavelet transform. The method presented is applicable to any quadratic QFT that need not be a conformal field theory (CFT). For thermal free scalar and Dirac field theories the resulting metric is that of (asymmetrically) warped Euclidean anti-de Sitter (AdS) space. For massless CFTs in the ground state, the geometry reduces to Euclidean AdS space reminiscent of the usual holographic correspondence. Certain parameters of the resulting geometry can be tuned by changing the shape of the wavelet function while maintaining the same type of geometry.