Towards a Reconstruction of General Bulk Metrics

TL;DR

This paper presents a covariant method to reconstruct the bulk metric of holographic spacetimes from boundary data using light-cone cuts, with implications for understanding subregion duality.

Contribution

It introduces a novel covariant reconstruction procedure for bulk metrics from boundary light-cone cuts, applicable to points in causal contact with the boundary.

Findings

Reconstruction of bulk metric up to conformal factor from boundary light-cone cuts.

Procedure to identify light-cone cuts from correlator divergences in dual field theory.

Discussion of extending the method to determine the full metric and outside the causal wedge.

Abstract

We prove that the metric of a general holographic spacetime can be reconstructed (up to an overall conformal factor) from distinguished spatial slices - "light-cone cuts" - of the conformal boundary. Our prescription is covariant and applies to bulk points in causal contact with the boundary. Furthermore, we describe a procedure for determining the light-cone cuts corresponding to bulk points in the causal wedge of the boundary in terms of the divergences of correlators in the dual field theory. Possible extensions for determining the conformal factor and including the cuts of points outside of the causal wedge are discussed. We also comment on implications for subregion/subregion duality.