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.
Highlights
The AdS/CFT correspondence [1] relates conformal field theories (CFTs) in d dimensions to gravitational theories in Anti de Sitter spacetimes in d + 1 dimensions (AdSd+1)
For large N CFTs with a large gap to higher spin operators, we show that the OPE between a local operator and the averaged null energy condition (ANEC) can be recast as a simple differential operator acting on the local operator
We have studied correlation functions of ANEC operators in states created by a local operator
Summary
The AdS/CFT correspondence [1] relates conformal field theories (CFTs) in d dimensions to gravitational theories in Anti de Sitter spacetimes in d + 1 dimensions (AdSd+1). This operator has remarkable properties, in particular its expectation value is positive for any state in the Hilbert space ψ| E |ψ ≥ 0 This inequality is known as the averaged null energy condition (ANEC) and is an astonishing property of quantum field theory. This signals that once the ANEC is satisfied no further information in terms of bounds should be accessible from the higher point correlation functions These operators were related in [41] by a conformal transformation to light-ray operators inserted at the conformal boundary of Minkowski space. We will show that the OPE expansion can be resummed to obtain an exact expression at finite distance between the ANEC operator and the local operator insertion This will allow us to compute the conformal collider higher point correlation functions for a large N CFT. Note added: while this paper was in preparation, we learned about [55] which contains some overlap with the results discussed here
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