What is the significance of the Gravity/CFT Correspondence in modern physics?

[marcus]

http://arxiv.org/abs/1105.0938
The gravity/CFT correspondence

Henrique Gomes, Sean Gryb, Tim Koslowski, Flavio Mercati
(Submitted on 4 May 2011)
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.
Comments: 5 pages, 1 figure
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My comment:
This work will be featured on 23 May at the first parallel session of Loops 2011, where there will be talks by three of the authors (plus a related one by Julian Barbour.)

 

[Schreiberdk]

I have a question here:

Could the classical conformal field theory be a classical statistical mechanics theory?

Edit: Just to be sure, doesn't conformal invariance mean an invariance under curved spacetime?

 

[Schreiberdk]

By the way; if I may specify: a 2+1 dimensional statistical mechanics theory, so it corresponds to the 3+1 dimensional gravity (General relativity) :)