Einstein gravity from ANEC correlators

• Main Authors: Alexandre Belin, Diego M. Hofman, Grégoire Mathys
• Format: Article
• Language: English
• Published: SpringerOpen 2019-08-01
• Series: Journal of High Energy Physics
• Subjects: AdS-CFT Correspondence; Conformal Field Theory; Anomalies in Field and String Theories
• Online Access: http://link.springer.com/article/10.1007/JHEP08(2019)032

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.