Einstein gravity from ANEC correlators. (English) Zbl 1421.83010
Summary: 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.
MSC:
| 83C05 | Einstein’s equations (general structure, canonical formalism, Cauchy problems) |
| 62P35 | Applications of statistics to physics |
| 81T40 | Two-dimensional field theories, conformal field theories, etc. in quantum mechanics |
| 81T50 | Anomalies in quantum field theory |
| 83C47 | Methods of quantum field theory in general relativity and gravitational theory |
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