Abstract
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.
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Belin, A., Hofman, D.M. & Mathys, G. Einstein gravity from ANEC correlators. J. High Energ. Phys. 2019, 32 (2019). https://doi.org/10.1007/JHEP08(2019)032
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DOI: https://doi.org/10.1007/JHEP08(2019)032