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.

[1]  Xi Dong,et al.  Bulk locality and quantum error correction in AdS/CFT , 2014, 1411.7041.

[2]  R. Bousso,et al.  UvA-DARE (Digital Academic Repository) Null Geodesics, Local CFT Operators and AdS/CFT for Subregions , 2013 .

[3]  V. Hubeny,et al.  Causal holographic information , 2012, 1204.1698.

[4]  Construction of local fields in the bulk of AdS 5 and other spaces , 1999, hep-th/9905186.

[5]  Holographic Probes of Anti-de Sitter Spacetimes , 1998, hep-th/9808017.

[6]  D. Lowe,et al.  Constructing local bulk observables in interacting AdS/CFT , 2011, 1102.2910.

[7]  T. Beth,et al.  Codes for the quantum erasure channel , 1996, quant-ph/9610042.

[8]  D. Sarkar,et al.  Holographic representation of bulk fields with spin in AdS/CFT , 2012, 1204.0126.

[9]  Shor,et al.  Scheme for reducing decoherence in quantum computer memory. , 1995, Physical review. A, Atomic, molecular, and optical physics.

[10]  J. Maldacena.  The Large-N Limit of Superconformal Field Theories and Supergravity , 1997, hep-th/9711200.

[11]  J. Polchinski,et al.  Bulk and transhorizon measurements in AdS/CFT , 2012, 1201.3664.

[12]  G. Lifschytz,et al.  Decoding the hologram: Scalar fields interacting with gravity , 2013, 1311.3020.

[13]  J. Polchinski,et al.  Higher Spin Holography, RG, and the Light Cone , 2014, 1411.3151.

[14]  Idse Heemskerk.  Construction of bulk fields with gauge redundancy , 2012, 1201.3666.

[15]  Holographic representation of local bulk operators , 2006, hep-th/0606141.

[16]  Daniel Gottesman,et al.  Stabilizer Codes and Quantum Error Correction , 1997, quant-ph/9705052.

[17]  F. Nogueira,et al.  The gravity dual of a density matrix , 2012, 1204.1330.

[18]  Stefan Leichenauer,et al.  AdS black holes, the bulk-boundary dictionary, and smearing functions , 2013, 1304.6821.

[19]  I. Morrison.  Boundary-to-bulk maps for AdS causal wedges and the Reeh-Schlieder property in holography , 2014, Journal of High Energy Physics.

[20]  AdS Dynamics from Conformal Field Theory , 1998, hep-th/9808016.

[21]  L. Susskind,et al.  Negative energy, superluminosity, and holography , 1999, hep-th/9903228.

[22]  R. Bousso,et al.  Light-sheets and AdS/CFT , 2012, 1203.6619.

[23]  A. Jevicki,et al.  AdS 4 / CFT 3 construction from collective fields , 2010, 1008.0633.

[24]  S. Rey,et al.  Scanning tunneling macroscopy, black holes and AdS/CFT bulk locality , 2014, 1403.3943.