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A toy model of black hole complementarity

  • Souvik Banerjee
  • Jan-Willem Bryan
  • Kyriakos Papadodimas
  • Suvrat Raju
Open Access
Regular Article - Theoretical Physics

Abstract

We consider the algebra of simple operators defined in a time band in a CFT with a holographic dual. When the band is smaller than the light crossing time of AdS, an entire causal diamond in the center of AdS is separated from the band by a horizon. We show that this algebra obeys a version of the Reeh-Schlieder theorem: the action of the algebra on the CFT vacuum can approximate any low energy state in the CFT arbitrarily well, but no operator within the algebra can exactly annihilate the vacuum. We show how to relate local excitations in the complement of the central diamond to simple operators in the band. Local excitations within the diamond are invisible to the algebra of simple operators in the band by causality, but can be related to complicated operators called “precursors”. We use the Reeh-Schlieder theorem to write down a simple and explicit formula for these precursors on the boundary. We comment on the implications of our results for black hole complementarity and the emergence of bulk locality from the boundary.

Keywords

AdS-CFT Correspondence Black Holes 1/N Expansion 

Notes

Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

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Copyright information

© The Author(s) 2016

Authors and Affiliations

  • Souvik Banerjee
    • 1
  • Jan-Willem Bryan
    • 1
  • Kyriakos Papadodimas
    • 1
    • 2
  • Suvrat Raju
    • 3
  1. 1.Van Swinderen Institute for Particle Physics and GravityUniversity of GroningenGroningenThe Netherlands
  2. 2.Theoretical Physics DepartmentCERNGeneva 23Switzerland
  3. 3.International Centre for Theoretical SciencesTata Institute of Fundamental ResearchBengaluruIndia

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