Einstein gravity from ANEC correlators

  • Alexandre Belin
  • Diego M. Hofman
  • Grégoire MathysEmail author
Open Access
Regular Article - Theoretical Physics


We study correlation functions with multiple averaged null energy (ANEC) operators in conformal field theories. For large N CFTs with a large gap to higher spin operators, we show that the OPE between a local operator and the ANEC can be recast as a particularly simple differential operator acting on the local operator. This operator is simple enough that we can resum it and obtain the finite distance OPE. Under the large N - large gap assumptions, the vanishing of the commutator of ANEC operators tightly constrains the OPE coefficients of the theory. An important example of this phenomenon is the conclusion that a = c in d = 4. This implies that the bulk dual of such a CFT is semi-classical Einstein-gravity with minimally coupled matter.


AdS-CFT Correspondence Conformal Field Theory Anomalies in Field and String Theories 


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) 2019

Authors and Affiliations

  1. 1.Institute for Theoretical PhysicsUniversity of AmsterdamAmsterdamThe Netherlands
  2. 2.CERN, Theory Division, 1 Esplanade des ParticulesGeneva 23Switzerland

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