Holographic Reconstruction and Renormalization in Asymptotically Ricci-flat Spacetimes

Abstract

In this work we elaborate on an extension of the AdS/CFT framework to a subclass of gravitational theories with vanishing cosmological constant. By building on earlier ideas, we construct a correspondence between Ricci-flat spacetimes admitting asymptotically hyperbolic hypersurfaces and a family of conformal field theories on a codimension two manifold at null infinity. By truncating the gravity theory to the pure gravitational sector, we find the most general spacetime asymptotics, renormalize the gravitational action, reproduce the holographic stress tensors and Ward identities of the family of CFTs and show how the asymptotics is mapped to and reconstructed from conformal field theory data. In even dimensions, the holographic Weyl anomalies identify the bulk time coordinate with the spectrum of central charges with characteristic length the bulk Planck length. Consistency with locality in the bulk time direction requires a notion of locality in this spectrum.