A 2D field theory equivalent to 3D gravity with no cosmological constant
Abstract
In (2+1) space-time dimensions the Einstein theory of gravity has no local degrees of freedom. In fact, in the presence of a negative cosmological term, it is described by a (1+1) dimensional theory living on its boundary: Liouville theory. It is invariant under the action of the two-dimensional conformal group, which, in the gravitational context, corresponds to the asymptotic symmetries of asymptotically AdS geometries. In the flat case, when the cosmological term is turned off, a theory describing gravity at the boundary is absent. In this note we show that, in the Hamiltonian setup, such a theory may be constructed. The theory is BMS3 invariant, as it should, corresponding to the asymptotic symmetry group of an asymptotically flat spacetime.
Keywords
Cite
@article{arxiv.1303.3568,
title = {A 2D field theory equivalent to 3D gravity with no cosmological constant},
author = {Glenn Barnich and Andrés Gomberoff and Hernán A. González},
journal= {arXiv preprint arXiv:1303.3568},
year = {2013}
}
Comments
4 pages. Contribution to the Proceedings of the Spanish Relativity Meeting ERE 2012