## SciPost Submission Page

# Bulk Locality and Asymptotic Causal Diamonds

### by Chethan Krishnan

#### This is not the current version.

### Submission summary

As Contributors: | Chethan Krishnan |

Arxiv Link: | https://arxiv.org/abs/1902.06709v1 |

Date submitted: | 2019-06-28 |

Submitted by: | Krishnan, Chethan |

Submitted to: | SciPost Physics |

Domain(s): | Theoretical |

Subject area: | High-Energy Physics - Theory |

### 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, ${\cal I}^{\pm}$. 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.

###### Current status:

### Submission & Refereeing History

## Reports on this Submission

### Anonymous Report 1 on 2019-9-2 Invited Report

### Report

In this manuscript, the author generalized the AdS-Rindler reconstruction of bulk operators to flat space by introducing the notion of an asymptotic causal diamond. The author observed that this could be a useful way of organizing quantum information in flat space holographically.

I have the following questions which I hope will help improve the clarity of the manuscript once they are addressed:

1. Is there an explicit reconstruction formula in an asymptotic causal diamond, in analogy with the HKLL formula in an AdS-Rindler wedge?

2. Is there a way to see the story work in a concrete example of flat space holography, such as the BFSS matrix model?

(in reply to Report 1 on 2019-09-02)

My (very incomplete) answers to the queries are below -

2. This is an interesting question that I have not been able to seriously consider yet. My first thoughts have been that perhaps one could relax the notion of the infinite momentum frame (IMF) used in the BFSS matrix model to an asymptotically infinite momentum frame (perhaps in the future and past). But while this would help connect with the asymptotic causal diamond idea, it is not clear to me that there is a manageable description of M-theory when one is away from the IMF. But it seems very likely (considering the crucial role played by the IMF in BFSS), that something like our asymptotic causal diamonds may play a role. One paper/review which I found to be thought-provoking for these types of considerations is Polchinski's hep-th/9903165, in particular section 4.