BV-BFV approach to General Relativity, Einstein-Hilbert action

Alberto S. Cattaneo, Michele Schiavina

Published 2015-09-18Version 1

The present paper shows that General Relativity in the ADM formalism admits a BV-BFV formulation in the sense of Cattaneo, Mnev and Reshetikhin. More precisely, for any $d+1\not=2$ (pseudo-)Riemannian manifold $M$ with spacelike or timelike boundary components, the BV theory on the bulk induces a compatible BFV theory on the boundary. As a byproduct, the usual canonical formulation of General Relativity is recovered in a straightforward way.