Revisiting holographic codes with fractal-like boundary erasures

TL;DR

This paper explores the properties of holographic fractal geometries, focusing on reconstruction wedges in various AdS/CFT contexts, and discusses implications for holography and complexity transfer.

Contribution

It extends the analysis of holographic codes to fractal geometries in higher dimensions and examines their reconstruction properties in black hole backgrounds.

Findings

Reconstruction wedges in AdS3/CFT2 align with vacuum-AdS approximations.

Clarification of straight and infinite boundary roles in higher-dimensional reconstruction.

Insights into uberholography through complexity transfer and one-shot holography.

Abstract

In this paper we investigate the code properties of holographic fractal geometries initiated in \cite{Pastawski:2016qrs}. We study reconstruction wedges in $AdS_3/CFT_2$ for black hole backgrounds, which are in qualitative agreement with the vacuum-AdS approximation using generalized entanglement entropy in \cite{Bao:2022tgv}. In higher dimensions, we study reconstruction wedges for the infinite, straight strip in $AdS_{d+1}/CFT_{d}$ and clarify the roles of `straight' and `infinite' in their code properties. Lastly, we comment on uberholography from the perspective of complexity transfer and one-shot holography.