Bounds on OPE Coefficients from Interference Effects in the Conformal Collider

TL;DR

This paper derives bounds on conformal field theory three-point function coefficients involving stress tensors and scalars using the average null energy condition, with implications for AdS duals and inflationary cosmology.

Contribution

It introduces new bounds on OPE coefficients in CFTs from interference effects, connecting them to gravitational anomalies and higher derivative terms in AdS and de-Sitter spaces.

Findings

Bounds on $raket{TT ext{O}}$ coefficients in CFTs.

Constraints on gravitational anomalies in 4D CFTs.

Implications for inflationary gravitational wave observables.

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, $\langle TT {\cal O } \rangle,$ 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 $\langle TT J \rangle$. 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 $\int \phi\hspace{.5mm} W^2 $. 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 $\phi \hspace{.5mm}W W^*$.