The gravity/CFT correspondence

TL;DR

This paper establishes a duality between gravity formulated as Shape Dynamics and a Weyl invariant boundary theory, providing new insights into gauge/gravity duality and supporting the AdS/CFT correspondence.

Contribution

It introduces a bulk/bulk duality in Shape Dynamics that naturally leads to a bulk/boundary duality, offering a gauge-invariant boundary definition and supporting gauge/gravity duality evidence.

Findings

Demonstrates a bulk/bulk duality in Shape Dynamics.

Derives a bulk/boundary duality consistent with AdS/CFT.

Provides gauge-invariant boundary formulation.

Abstract

General Relativity can be formulated in terms of a spatially Weyl invariant gauge theory called Shape Dynamics. Using this formulation, we establish a "bulk/bulk" duality between gravity and a Weyl invariant theory on spacelike Cauchy hypersurfaces. This duality has two immediate consequences: i) it leads trivially to a corresponding "bulk/boundary" duality between General Relativity and a boundary CFT, and ii) the boundary can be defined in a gauge-invariant way. Moreover, the corresponding bulk/boundary duality is sufficient to explain a large portion of the evidence in favor of gauge/gravity duality and provides independent evidence for the AdS/CFT correspondence.