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Title: Boundary dual of bulk local operators

Publication Date:
Sponsoring Org.:
USDOE Office of Science (SC), High Energy Physics (HEP) (SC-25)
OSTI Identifier:
Grant/Contract Number:
Resource Type:
Journal Article: Publisher's Accepted Manuscript
Journal Name:
Physical Review D
Additional Journal Information:
Journal Volume: 96; Journal Issue: 2; Related Information: CHORUS Timestamp: 2017-07-11 05:02:10; Journal ID: ISSN 2470-0010
American Physical Society
Country of Publication:
United States

Citation Formats

Sanches, Fabio, and Weinberg, Sean J. Boundary dual of bulk local operators. United States: N. p., 2017. Web. doi:10.1103/PhysRevD.96.026004.
Sanches, Fabio, & Weinberg, Sean J. Boundary dual of bulk local operators. United States. doi:10.1103/PhysRevD.96.026004.
Sanches, Fabio, and Weinberg, Sean J. Mon . "Boundary dual of bulk local operators". United States. doi:10.1103/PhysRevD.96.026004.
title = {Boundary dual of bulk local operators},
author = {Sanches, Fabio and Weinberg, Sean J.},
abstractNote = {},
doi = {10.1103/PhysRevD.96.026004},
journal = {Physical Review D},
number = 2,
volume = 96,
place = {United States},
year = {Mon Jul 10 00:00:00 EDT 2017},
month = {Mon Jul 10 00:00:00 EDT 2017}

Journal Article:
Free Publicly Available Full Text
This content will become publicly available on July 10, 2018
Publisher's Accepted Manuscript

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Cited by: 4works
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  • We develop the representation of local bulk fields in anti-de Sitter (AdS) space by nonlocal operators on the boundary, working in the semiclassical limit and using AdS{sub 2} as our main example. In global coordinates we show that the boundary operator has support only at points which are spacelike separated from the bulk point. We construct boundary operators that represent local bulk operators inserted behind the horizon of the Poincare patch and inside the Rindler horizon of a two-dimensional black hole. We show that these operators respect bulk locality and comment on the generalization of our construction to higher dimensionalmore » AdS black holes.« less
  • Here, we formulate a minimum requirement for CFT operators to be localized in the dual AdS. In any spacetime dimensions, we show that a general solution to the requirement is a linear superposition of operators creating spherical boundaries in CFT, with the dilatation by the imaginary unit from their centers. This generalizes the recent proposal by Miyaji et al. for bulk local operators in the three dimensional AdS. We show that Ishibashi states for the global conformal symmetry in any dimensions and with the imaginary di-latation obey free field equations in AdS and that incorporating bulk interactions require their superpositions.more » We also comment on the recent proposals by Kabat et al., and by H. Verlinde.« less
  • The Lorentzian anti-de Sitter/conformal field theory correspondence implies a map between local operators in supergravity and nonlocal operators in the CFT. By explicit computation we construct CFT operators which are dual to local bulk fields in the semiclassical limit. The computation is done for general dimension in global, Poincare and Rindler coordinates. We find that the CFT operators can be taken to have compact support in a region of the complexified boundary whose size is set by the bulk radial position. We show that at finite N the number of independent commuting operators localized within a bulk volume saturates themore » holographic bound.« less
  • 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 finitemore » 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.« less
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