Caustics bounding entanglement wedges

TL;DR

This paper investigates caustics on entanglement wedge boundaries in AdS3 holography, revealing how caustics can cause sharp corners and breakdowns in boundary-to-bulk operator identification procedures.

Contribution

It identifies and analyzes caustics terminating lightsheets in specific spacetimes, showing their impact on entanglement wedge shapes and boundary operator localization.

Findings

Caustics can create sharp corners in entanglement wedges.

Certain caustics cause the breakdown of boundary operator identification procedures.

The shape of entanglement wedges can be more complex due to caustics.

Abstract

We study the caustics on the boundaries of entanglement wedges in the context of holography in asymptotically AdS$_3$ 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 [arXiv:1703.07780] 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.