A 2D field theory equivalent to 3D gravity with no cosmological constant

TL;DR

This paper constructs a boundary theory for (2+1)-dimensional flat spacetime gravity, demonstrating its BMS3 invariance and providing a new perspective on flat space holography.

Contribution

It introduces a Hamiltonian boundary theory for 3D flat space gravity, filling the gap where no boundary theory was previously known.

Findings

The boundary theory is BMS3 invariant.

It provides a holographic description for flat space gravity.

The theory is constructed explicitly in the Hamiltonian framework.

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.