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Title: Local bulk operators in AdS/CFT correspondence: A holographic description of the black hole interior

Abstract

To gain insight into how bulk locality emerges from the holographic conformal field theory (CFT), we reformulate the bulk-to-boundary map in as local a way as possible. In previous work, we carried out this program for Lorentzian anti-de Sitter (AdS), and showed the support on the boundary could always be reduced to a compact region spacelike separated from the bulk point. In the present work the idea is extended to a complexified boundary, where spatial coordinates are continued to imaginary values. This continuation enables us to represent a local bulk operator as a CFT operator with support on a finite disc on the complexified boundary. We treat general AdS in Poincare coordinates and AdS{sub 3} in Rindler coordinates. We represent bulk operators inside the horizon of a Banados-Teitelboim-Zanelli (BTZ) black hole and we verify that the correct bulk two-point functions are reproduced, including the divergence when one point hits the BTZ singularity. We comment on the holographic description of black holes formed by collapse and discuss locality and holographic entropy counting at finite N.

Authors:
;  [1];  [2];  [3]
  1. Department of Physics, Columbia University, New York, New York 10027 (United States)
  2. Department of Mathematics and Physics and CCMSC, University of Haifa at Oranim, Tivon 36006 (Israel)
  3. Department of Physics, Brown University, Providence, Rhode Island 02912 (United States)
Publication Date:
OSTI Identifier:
20935275
Resource Type:
Journal Article
Journal Name:
Physical Review. D, Particles Fields
Additional Journal Information:
Journal Volume: 75; Journal Issue: 10; Other Information: DOI: 10.1103/PhysRevD.75.106001; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0556-2821
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; ANTI DE SITTER SPACE; BLACK HOLES; CONFORMAL INVARIANCE; COORDINATES; ENTROPY; HOLOGRAPHY; LOCALITY; MAPS; QUANTUM FIELD THEORY; SINGULARITY

Citation Formats

Hamilton, Alex, Kabat, Daniel, Lifschytz, Gilad, and Lowe, David A. Local bulk operators in AdS/CFT correspondence: A holographic description of the black hole interior. United States: N. p., 2007. Web. doi:10.1103/PHYSREVD.75.106001.
Hamilton, Alex, Kabat, Daniel, Lifschytz, Gilad, & Lowe, David A. Local bulk operators in AdS/CFT correspondence: A holographic description of the black hole interior. United States. doi:10.1103/PHYSREVD.75.106001.
Hamilton, Alex, Kabat, Daniel, Lifschytz, Gilad, and Lowe, David A. Tue . "Local bulk operators in AdS/CFT correspondence: A holographic description of the black hole interior". United States. doi:10.1103/PHYSREVD.75.106001.
@article{osti_20935275,
title = {Local bulk operators in AdS/CFT correspondence: A holographic description of the black hole interior},
author = {Hamilton, Alex and Kabat, Daniel and Lifschytz, Gilad and Lowe, David A},
abstractNote = {To gain insight into how bulk locality emerges from the holographic conformal field theory (CFT), we reformulate the bulk-to-boundary map in as local a way as possible. In previous work, we carried out this program for Lorentzian anti-de Sitter (AdS), and showed the support on the boundary could always be reduced to a compact region spacelike separated from the bulk point. In the present work the idea is extended to a complexified boundary, where spatial coordinates are continued to imaginary values. This continuation enables us to represent a local bulk operator as a CFT operator with support on a finite disc on the complexified boundary. We treat general AdS in Poincare coordinates and AdS{sub 3} in Rindler coordinates. We represent bulk operators inside the horizon of a Banados-Teitelboim-Zanelli (BTZ) black hole and we verify that the correct bulk two-point functions are reproduced, including the divergence when one point hits the BTZ singularity. We comment on the holographic description of black holes formed by collapse and discuss locality and holographic entropy counting at finite N.},
doi = {10.1103/PHYSREVD.75.106001},
journal = {Physical Review. D, Particles Fields},
issn = {0556-2821},
number = 10,
volume = 75,
place = {United States},
year = {2007},
month = {5}
}