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

Eric Mintun¹, Joseph Polchinski^1,2, Vladimir Rosenhaus²

¹Department of Physics, University of California, Santa Barbara, California 93106-9530, USA.

Physical Review Letters

|November 10, 2015

Summary

Quantum error correction explains bulk information localization in boundary duals. Incorporating gauge invariance reveals this structure, linking it to spacetime emergence and bulk field nonuniqueness.

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Area of Science:

Theoretical Physics
Quantum Gravity
String Theory

Background:

Recent work by Almheiri, Dong, and Harlow proposed quantum error correction as a framework for understanding bulk information localization in boundary duals.
The concept of bulk-locality in holographic theories remains a key area of investigation.
Understanding the relationship between boundary properties and emergent spacetime is crucial.

Purpose of the Study:

To demonstrate how gauge invariance in the boundary theory naturally incorporates the quantum error correction structure.
To provide a new perspective on the nonuniqueness of bulk fields (precursors).
To explore the connection between gauge invariance and the emergence of spacetime.

Main Methods:

Analysis of the interplay between gauge invariance and quantum error correction in the context of boundary dualities.
Investigating the mathematical structure arising from the incorporation of gauge symmetry.
Examining the implications for the definition and properties of bulk fields.

Main Results:

The quantum error correction structure for bulk information localization emerges naturally when boundary gauge invariance is considered.
This framework offers a novel explanation for the nonuniqueness of bulk fields (precursors).
A direct link is established between gauge invariance and the emergence of spacetime geometry.

Conclusions:

Gauge invariance is fundamental to understanding bulk locality via quantum error correction in holographic theories.
The study deepens our insight into the holographic principle and the construction of spacetime from boundary degrees of freedom.
This work suggests that gauge symmetries play a critical role in the emergence of spacetime itself.