# Bulk Locality and Asymptotic Causal Diamonds

### 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 Discipline: Physics Subject area: High-Energy Physics - Theory Approach: Theoretical

### 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.

### Ontology / Topics

See full Ontology or Topics database.

###### Current status:
Has been resubmitted

### Submission & Refereeing History

Resubmission 1902.06709v2 on 9 September 2019
Submission 1902.06709v1 on 28 June 2019

## Reports on this Submission

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

• Cite as: Anonymous, Report on arXiv:1902.06709v1, delivered 2019-09-02, doi: 10.21468/SciPost.Report.1146

### 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?

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Author Chethan Krishnan on 2019-09-10
(in reply to Report 1 on 2019-09-02)
Category:
remark
pointer to related literature

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

1. Unfortunately, in dimensions higher than 1+1, the wave equation in our generalized Rindler wedge coordinates is not separable. But it is possible to argue that the reconstruction must exist, because this is essentially an existence problem for solutions of hyperbolic PDEs in regions where one does not have to cross charecteristic (ie., null) surfaces etc. A paper where we give a detailed analysis of the "holographic content" in this sense, of an asymptotic casual diamond in general dimensions, is currently in preparation. The basic idea is as outlined in the Appendix of the present paper.

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.