Abstract
We study the caustics on the boundaries of entanglement wedges in the context of holography in asymptotically AdS3 spacetimes. These entanglement wedges play an important role in our understanding of the emergence of bulk locality. A procedure was proposed by Sanches and Weinberg for identifying boundary operators which are local in the bulk, which also applies to certain regions that lie beyond the reach of HRT surfaces by taking advantage of the lightsheets which bound entanglement wedges. We identify the caustics which terminate these lightsheets in conical deficit and BTZ black hole spacetimes and find that in some examples these caustics lead to a sharp corner in the entanglement wedge. The unexpected shape of these entanglement wedges leads, in those cases, to a breakdown of this procedure. Many of the properties of the rich variety of caustics possible in higher dimensions remains to be explored which, as this work demonstrates, could lead to more unexpected features in the shapes of entanglement wedges.
Highlights
This analysis does not have anything to say about whether the operators are localised at points in the bulk, it just restricts them to the entanglement wedge
We study the caustics on the boundaries of entanglement wedges in the context of holography in asymptotically AdS3 spacetimes
A procedure was proposed by Sanches and Weinberg for identifying boundary operators which are local in the bulk, which applies to certain regions that lie beyond the reach of HRT surfaces by taking advantage of the lightsheets which bound entanglement wedges
Summary
Let us start by collecting the necessary notation. We will consider spacetimes, M , which are asymptotically AdS. It was argued in [15] that, even in the presence of an entanglement shadow, the entire bulk is in the localisable region when entanglement wedges probe the entire spacetime This argument was based on an implicit assumption on the geometry of entanglement wedges, namely that the future and past boundaries of a cross-section of the entanglement wedge as depicted in figure 1 are monotonic. We investigate this assumption by deriving the precise form of entanglement wedges and the caustics bounding them in asymptotically-AdS3 geometries using the embedding space formalism This will allow us to identify the non-localisable regions in some simple spacetimes by using the techniques proposed in [15]. When given access to only one asymptotic region, as is the case for black holes formed by collapse, we find that there is a non-localisable region near the horizon which coincides with the entanglement shadow present in that case
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