Abstract
We develop a formalism to study the implications of causality on OPE coefficients in conformal field theories with large central charge and a sparse spectrum of higher spin operators. The formalism has the interpretation of a new conformal collider-type experiment for these class of CFTs and hence it has the advantage of requiring knowledge only about CFT three-point functions. This is accomplished by considering the holographic null energy operator which was introduced in [1] as a generalization of the averaged null energy operator. Analyticity properties of correlators in the Regge limit imply that the holographic null energy operator is a positive operator in a subspace of the total CFT Hilbert space. Utilizing this positivity condition, we derive bounds on three-point functions 〈TO1O2〉 of the stress tensor with various operators for CFTs with large central charge and a sparse spectrum. After imposing these constraints, we also find that the operator product expansions of all primary operators in the Regge limit have certain universal properties. All of these results are consistent with the expectation that CFTs in this class, irrespective of their microscopic details, admit universal gravity-like holographic dual descriptions. Furthermore, this connection enables us to constrain various inflationary observables such as the amplitude of chiral gravity waves, non-gaussanity of gravity waves and tensor-to-scalar ratio.
Highlights
In conformal field theory (CFT), causality of four-point functions places nontrivial constraints on CFT three-point couplings
We develop a formalism to study the implications of causality on OPE coefficients in conformal field theories with large central charge and a sparse spectrum of higher spin operators
The formalism has the interpretation of a new conformal collider-type experiment for these class of CFTs and it has the advantage of requiring knowledge only about CFT three-point functions
Summary
In conformal field theory (CFT), causality of four-point functions places nontrivial constraints on CFT three-point couplings. The same constraints were derived in [45, 46] by imposing unitarity on a differently smeared correlator ψψTαβTγδ in the Regge limit This approach was recently extended to study a mixed system of four-point functions in the Regge limit yielding new bounds on the OPE coefficients of low spin operators in holographic CFTs [8]. After imposing these causality constraints, we find that the expectation value of the holographic null energy operator is universal and it is completely determined by the lightcone limit result This observation suggests the following conclusion about the operator product expansions in holographic CFTs: 5This formalism can be adapted to computing the contribution of any conformal multiplet to the Regge limit of four-point correlation functions.
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