The gravity/CFT correspondence

Details The gravity/CFT correspondence The gravity/CFT correspondence

2011-05-04

arxiv.org/abs/1105.0938v1

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

5 pages, 1 figure

Scientific paper

We prove a general correspondence between classical gravity in 3+1 dimensions and a pair of classical conformal field theories in 3 dimensions (the generalization to higher dimensions is straightforward). The proof relies on a novel formulation of general relativity called shape dynamics that, despite having different local symmetries, leads to classical trajectories identical to those of general relativity in a particular gauge. The key difference is that general relativity's refoliation invariance is traded for volume-preserving three-dimensional conformal invariance, i.e., local spatial Weyl invariance. It is precisely this symmetry that allows us to establish the general correspondence while resolving exactly the local degrees of freedom, a feat that is not possible in general relativity, without a derivative expansion, due to non-linearity.

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