Vacuum energy in asymptotically flat 2Â +Â 1 gravity

We compute the vacuum energy of three-dimensional asymptotically flat space based on a Chern-Simons formulation for the Poincaré group. The equivalent action is nothing but the Einstein-Hilbert term in the bulk plus half of the Gibbons-Hawking term at the boundary. The derivation is based on the evaluation of the Noether charges in the vacuum. We obtain that the vacuum energy of this space has the same value as the one of the asymptotically flat limit of three-dimensional anti-de Sitter space.