A Shape Dynamical Approach to Holographic Renormalization

TL;DR

This paper explores how Shape Dynamics, a conformal gravity theory, offers a classical mechanism to understand holographic renormalization and dualities like AdS/CFT, providing an alternative perspective on gravity and field theory correspondence.

Contribution

It demonstrates that gauge symmetry trading in Shape Dynamics can explain holographic renormalization results, offering an alternative to the AdS/CFT conjecture.

Findings

Shape Dynamics provides a classical mechanism for holographic renormalization.

The classical equivalence suggests a duality between gravity's radial evolution and RG flow.

Shape Dynamics emphasizes conformal structure as fundamental in gravity.

Abstract

We provide a bottom-up argument to derive some known results from holographic renormalization using the classical bulk-bulk equivalence of General Relativity and Shape Dynamics, a theory with spatial conformal (Weyl) invariance. The purpose of this paper is twofold: 1) to advertise the simple classical mechanism: trading of gauge symmetries, that underlies the bulk-bulk equivalence of General Relativity and Shape Dynamics to readers interested in dualities of the type of AdS/CFT; and 2) to highlight that this mechanism can be used to explain certain results of holographic renormalization, providing an alternative to the AdS/CFT conjecture for these cases. To make contact with usual the semiclassical AdS/CFT correspondence, we provide, in addition, a heuristic argument that makes it plausible why the classical equivalence between General Relativity and Shape Dynamics turns into a duality between radial evolution in gravity and the renormalization group flow of a conformal field theory. We believe that Shape Dynamics provides a new perspective on gravity by giving conformal structure a primary role within the theory. It is hoped that this work provides the first steps towards understanding what this new perspective may be able to teach us about holographic dualities.