Precursors, Gauge Invariance, and Quantum Error Correction in AdS/CFT

TL;DR

This paper explores how gauge invariance and entanglement in the boundary CFT relate to the ambiguity in reconstructing bulk operators in AdS/CFT, demonstrating the connection through a simple model and quantum error correction concepts.

Contribution

It explicitly shows how gauge invariance leads to precursor localization freedom and links this to quantum error correction in the context of AdS/CFT.

Findings

Gauge invariance manifests as smearing function freedom.

Precursor localization can be varied spatially.

Quantum error correction explains the operator ambiguity.

Abstract

A puzzling aspect of the AdS/CFT correspondence is that a single bulk operator can be mapped to multiple different boundary operators, or precursors. By improving upon a recent model of Mintun, Polchinski, and Rosenhaus, we demonstrate explicitly how this ambiguity arises in a simple model of the field theory. In particular, we show how gauge invariance in the boundary theory manifests as a freedom in the smearing function used in the bulk-boundary mapping, and explicitly show how this freedom can be used to localize the precursor in different spatial regions. We also show how the ambiguity can be understood in terms of quantum error correction, by appealing to the entanglement present in the CFT. The concordance of these two approaches suggests that gauge invariance and entanglement in the boundary field theory are intimately connected to the reconstruction of local operators in the dual spacetime.