BV-BFV approach to general relativity: Einstein-Hilbert action

The present paper shows that general relativity in the Arnowitt-Deser-Misner formalism admits a BV-BFV formulation. More precisely, for any d + 1 ≠ 2 (pseudo-) Riemannian manifold M with space-like or time-like boundary components, the BV data on the bulk induces compatible BFV data on the boundary. As a byproduct, the usual canonical formulation of general relativity is recovered in a straightforward way.