Modest holography and bulk reconstruction in asymptotically flat spacetimes

TL;DR

This paper proposes a modest holographic method for reconstructing bulk geometry in asymptotically flat spacetimes using boundary two-point correlators, relying on free field correspondences and Hadamard expansion.

Contribution

It introduces a new approach to bulk reconstruction in flat spacetimes based on boundary correlators and free field correspondence, distinct from AdS/CFT duality.

Findings

Bulk-to-boundary correspondence for free quantum fields

Bulk metric reconstruction via Hadamard expansion

Applicable to generic asymptotically flat spacetimes

Abstract

In this work we present a "modest" holographic reconstruction of the bulk geometry in asymptotically flat spacetime using the two-point correlators of boundary quantum field theory (QFT) in asymptotically flat spacetime. The boundary QFT lives on the null boundary of the spacetime, namely null infinity and/or the Killing horizons. The bulk reconstruction relies on two unrelated results: (i) there is a bulk-to-boundary type correspondence between free quantum fields living in the bulk manifold and free quantum fields living on its null boundary, and (ii) one can construct the metric by making use of the Hadamard expansion of the field living in the bulk. This holographic reconstruction is "modest" in that the fields used are non-interacting and not strong-weak holographic duality in the sense of AdS/CFT, but it works for generic asymptotically flat spacetime subject to some reasonably mild conditions.