Spacetime and the Holographic Renormalization Group

TL;DR

This paper proposes a holographic framework linking theories on nested AdS surfaces to quantum gravity, with renormalization group flows capturing bulk geometric information.

Contribution

It introduces a novel holographic correspondence between surface theories and bulk quantum gravity, using RG flows to encode spacetime geometry.

Findings

RG flows describe the relationship between surface theories and bulk geometry

Foliation dependence encodes the bulk spacetime structure

New perspective on holography in AdS spaces

Abstract

Anti-de Sitter (AdS) space can be foliated by a family of nested surfaces homeomorphic to the boundary of the space. We propose a holographic correspondence between theories living on each surface in the foliation and quantum gravity in the enclosed volume. The flow of observables between our ``interior'' theories is described by a renormalization group equation. The dependence of these flows on the foliation of space encodes bulk geometry.