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Local bulk physics from intersecting modular Hamiltonians

  • Daniel Kabat
  • Gilad Lifschytz
Open Access
Regular Article - Theoretical Physics

Abstract

We show that bulk quantities localized on a minimal surface homologous to a boundary region correspond in the CFT to operators that commute with the modular Hamiltonian associated with the boundary region. If two such minimal surfaces intersect at a point in the bulk then CFT operators which commute with both extended modular Hamiltonians must be localized at the intersection point. We use this to construct local bulk operators purely from CFT considerations, without knowing the bulk metric, using intersecting modular Hamiltonians. For conformal field theories at zero and finite temperature the appropriate modular Hamiltonians are known explicitly and we recover known expressions for local bulk observables.

Keywords

AdS-CFT Correspondence Conformal Field Theory 

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) 2017

Authors and Affiliations

  1. 1.Department of Physics and Astronomy, Lehman CollegeCity University of New YorkBronxU.S.A.
  2. 2.Department of Mathematics and Haifa Research Center for Theoretical Physics and AstrophysicsUniversity of HaifaHaifaIsrael

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