SciPost Phys. 7, 057 (2019) ·
published 29 October 2019

· pdf
In AdS/CFT, the nonuniqueness 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, ${\cal I}^{\pm}$. We
observe that for flat space with an IR cutoff, 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 subadditivity, 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 cutoff, 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 subfactors of
Hilbert spaces of holographic theories.
Prof. Krishnan: "My (very incomplete) answers t..."
in Report on Bulk Locality and Asymptotic Causal Diamonds