# Bulk Locality and Asymptotic Causal Diamonds

## TL;DR

This paper introduces asymptotic causal diamonds in flat space, exploring their role in holography, bulk reconstruction, and entanglement entropy, revealing structural similarities to AdS/CFT and potential for broader spacetime applications.

## Contribution

It proposes asymptotic causal diamonds as a new framework for flat space holography, connecting boundary data, entanglement, and error correction concepts.

## Key findings

- ACDs encode boundary subregions for flat space holography
- ACDs lead to a consistent flat space entanglement entropy
- Bulk union/intersection structures mirror quantum error correction principles

## Abstract

In AdS/CFT, the non-uniqueness of the reconstructed bulk from boundary subregions has motivated the notion of code subspaces. We present some closely related structures that arise in flat space. A useful organizing idea is that of an {\em asymptotic} causal diamond (ACD): a causal diamond attached to the conformal boundary of Minkowski space. The space of ACDs is defined by pairs of points, one each on the future and past null boundaries, ${\cal I}^{\pm}$. We observe that for flat space with an IR cut-off, this space (a) encodes a preferred class of boundary ``subregions'', (b) is a plausible way to capture holographic data for local bulk reconstruction, (c) has a natural interpretation as the kinematic space for holography, (d) leads to a holographic entanglement entropy in flat space that matches previous definitions and satisfies strong sub-additivity, and, (e) has a bulk union/intersection structure isomorphic to the one that motivated the introduction of quantum error correction in AdS/CFT. By sliding the cut-off, we also note one substantive way in which flat space holography differs from that in AdS. Even though our discussion is centered around flat space (and AdS), we note that there are notions of ACDs in other spacetimes as well. They could provide a covariant way to abstractly characterize tensor sub-factors of Hilbert spaces of holographic theories.