Abstract
We apply the average null energy condition to obtain upper bounds on the three-point function coefficients of stress tensors and a scalar operator, leftlangle TTmathcal{O}rightrangle , in general CFTs. We also constrain the gravitational anomaly of U(1) currents in four-dimensional CFTs, which are encoded in three-point functions of the form 〈T T J 〉. In theories with a large N AdS dual we translate these bounds into constraints on the coefficient of a higher derivative bulk term of the form ∫ϕ W2. We speculate that these bounds also apply in de-Sitter. In this case our results constrain inflationary observables, such as the amplitude for chiral gravity waves that originate from higher derivative terms in the Lagrangian of the form ϕ W W∗.
Highlights
We constrain the gravitational anomaly of U(1) currents in four-dimensional CFTs, which are encoded in three-point functions of the form T T J
In this paper we investigate some implications of the average null energy condition in conformal field theories
Requiring that the energy flux is positive imposes constraints on the three-point function coefficients
Summary
In this paper we investigate some implications of the average null energy condition in conformal field theories. Requiring that the total contribution to the energy flux is positive imposes a nontrivial upper bound on the absolute magnitude of this three-point correlator We apply these ideas to general scalar operators O as well as conserved currents with spin one, J, where we use it to put bounds on the gravitational anomaly in d = 4 CFTs. Because the bound arises from quantum mechanical interference effects, these bounds are stronger than those obtained in states created by a single primary local operator and its descendants (though the resulting bounds involve more OPE coefficients). Because the bound arises from quantum mechanical interference effects, these bounds are stronger than those obtained in states created by a single primary local operator and its descendants (though the resulting bounds involve more OPE coefficients) This energy flux at infinity is given by an integral of the stress tensor. In the appendices we include more explicit derivations of the material in the main sections
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