Einstein gravity as a 3D conformally invariant theory
Oct, 2010
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Abstract: (arXiv)
We give an alternative description of the physical content of general relativity that does not require a Lorentz invariant spacetime. Instead, we find that gravity admits a dual description in terms of a theory where local size is irrelevant. The dual theory is invariant under foliation preserving 3-diffeomorphisms and 3D conformal transformations that preserve the 3-volume (for the spatially compact case). Locally, this symmetry is identical to that of Horava-Lifshitz gravity in the high energy limit but our theory is equivalent to Einstein gravity. Specifically, we find that the solutions of general relativity, in a gauge where the spatial hypersurfaces have constant mean extrinsic curvature, can be mapped to solutions of a particular gauge fixing of the dual theory. Moreover, this duality is not accidental. We provide a general geometric picture for our procedure that allows us to trade foliation invariance for conformal invariance. The dual theory provides a new proposal for the theory space of quantum gravity.Note:
- 27 pages. Published version (minor changes and corrections)
- dimension: 3
- invariance: conformal
- duality
- foliation
- gravitation: model
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