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 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, I^{\pm}I±. 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.
Highlights
We will start by observing a few reasons to believe that holography is likely to be a universal feature of quantum gravity1
The idea of taking asymptotic causal diaomnds seriously for holographic purposes beyond AdS/CFT is likely to be fruitful: we will present developments along multiple directions using these ideas in some follow up papers [19, 20], but will limit ourselves in this paper to making clear that the local bulk structure that arises from them in flat space is isomorphic in many ways to that which arises in AdS holography
Asymptotic Causal Diamonds: Our goal is to construct an analogue of Rindler-AdS/entanglement wedge reconstrcution, that is useful in flat space
Summary
We will start by observing a few reasons to believe that holography is likely to be a universal feature of quantum gravity. At least at the semi-classical level, in asymptotically AdS spaces we know how to formulate a correspondence between bulk calculations and boundary calculations [5] This is in big parts due to the fact that the holographic boundary in AdS/CFT is as close to a physical boundary as one can hope for. The idea of taking asymptotic causal diaomnds seriously for holographic purposes beyond AdS/CFT is likely to be fruitful: we will present developments along multiple directions using these ideas in some follow up papers [19, 20], but will limit ourselves in this paper to making clear that the local bulk structure that arises from them in flat space is isomorphic in many ways to that which arises in AdS holography. Our work is closely related to the HRT construction [12]: the choice of a point each on the two null boundaries defines a canonical class of HRT surfaces for flat space with a cut-off
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