Bulk-Boundary Duality, Gauge Invariance, and Quantum Error Correction

TL;DR

This paper explores how gauge invariance in boundary theories naturally leads to quantum error correction structures, offering insights into bulk-boundary duality and the emergence of spacetime in holography.

Contribution

It demonstrates that gauge invariance inherently produces quantum error correction structures, clarifying the non-uniqueness of bulk fields and linking gauge invariance to spacetime emergence.

Findings

Gauge invariance naturally encodes quantum error correction.

Bulk field non-uniqueness is explained by gauge invariance.

Provides a new perspective on bulk-boundary duality.

Abstract

Recently, Almheiri, Dong, and Harlow have argued that the localization of bulk information in a boundary dual should be understood in terms of quantum error correction. We show that this structure appears naturally when the gauge invariance of the boundary theory is incorporated. This provides a new understanding of the non-uniqueness of the bulk fields (precursors). It suggests a close connection between gauge invariance and the emergence of spacetime.