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

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 nonuniqueness of the bulk fields (precursors). It suggests a close connection between gauge invariance and the emergence of spacetime.