Gravity/CFT correspondence

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In summary, the authors present a general correspondence between classical gravity in 3+1 dimensions and a pair of classical conformal field theories in 3 dimensions. This is achieved through a novel formulation of general relativity called shape dynamics, which replaces general relativity's refoliation invariance with volume-preserving three-dimensional conformal invariance. The proof relies on a specific gauge and resolves the local degrees of freedom. The work will be presented at a conference and the authors discuss the possibility of the classical conformal field theory being a classical statistical mechanics theory.
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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.)
 
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  • #2
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?
 
  • #3
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) :)
 

1. What is the "Gravity/CFT correspondence"?

The "Gravity/CFT correspondence" is a theoretical framework that suggests a mathematical relationship between two seemingly different physical theories: general relativity, which describes gravity on a large scale, and conformal field theory, which describes the behavior of quantum fields on a much smaller scale.

2. How does the Gravity/CFT correspondence work?

The Gravity/CFT correspondence suggests that a higher-dimensional theory of gravity, such as string theory, is equivalent to a lower-dimensional quantum field theory. This means that the two theories are different descriptions of the same underlying physical reality.

3. What is the significance of the Gravity/CFT correspondence?

The Gravity/CFT correspondence is significant because it offers a potential solution to one of the biggest challenges in theoretical physics: reconciling general relativity and quantum mechanics. It also provides a framework for understanding the nature of spacetime and the fundamental building blocks of the universe.

4. How was the Gravity/CFT correspondence discovered?

The Gravity/CFT correspondence was first proposed in the late 1990s by physicists Juan Maldacena, Edward Witten, and others. It emerged from various developments in string theory, which suggested that gravity could be described in terms of lower-dimensional quantum field theories.

5. What are the implications of the Gravity/CFT correspondence?

The Gravity/CFT correspondence has far-reaching implications for our understanding of the universe, from the behavior of black holes to the nature of time and space. It also has potential applications in other areas of physics, such as condensed matter physics and cosmology.

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