Einstein gravity as a 3D conformally invariant theory

TL;DR

This paper presents a dual formulation of Einstein gravity as a 3D conformally invariant theory, removing the need for Lorentz invariance and offering new insights into quantum gravity.

Contribution

It introduces a dual description of general relativity with 3D conformal invariance, linking solutions via gauge fixing and proposing a novel approach to quantum gravity.

Findings

Gravity admits a dual description with 3D conformal invariance.

Solutions of Einstein gravity can be mapped to solutions of the dual theory.

The duality provides a new perspective on the theory space of quantum gravity.

Abstract

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.