Bounds on OPE Coefficients from Interference Effects in the Conformal Collider

TL;DR

This work leverages the average null energy condition within the conformal collider framework to derive universal bounds on TT𝒪 and TTJ OPE coefficients in CFTs, including explicit sum rules with a Δ-dependent weight f(Δ). It translates these bounds into constraints on bulk AdS EFT couplings via a χ W² interaction and extends the logic to de-Sitter, yielding quasi-bounds that constrain inflationary chiral gravity waves and deviations from the standard consistency relation. The analysis encompasses general d≥4 and d=3 cases, with concrete applications to large-N CS-matter theories and the 3d Ising model, and provides SUSY-assisted refinements in d=4. Overall, the paper links quantum energy positivity to concrete bounds on CFT data, holographic couplings, and cosmological observables, offering testable predictions across high-energy and early-universe contexts.

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 φ\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 $φ\hspace{.5mm}W W^*$.

Figures (3)

• Figure 1: In the conformal collider experiment (a), the energy created by a localized excitation (blue) is measured far away by a calorimeter (red). (b) For a CFT, this is equivalent to measuring the energy at null infinity $\mathcal{J}^+$.
• Figure 2: We consider operators with zero spatial momentum that create a pair of free particles. In (a,b,c) we consider a stress tensor operator. We examine the wavefunction along the direction specified by the long arrow and we decompose the stress tensor according to the spin around that axis. (a) The spin zero state is obtained for scalars, spin one for fermions (b) and spin two for vectors or self-dual forms (c). (d) is the state produced by a scalar operator with can interfere with (a). (e) is produced by a current with spin one along the observation axis and can interfere with (b). Finally (f) is a current with spin zero along the observation axis in a theory of scalars. It produces two different real scalars in the back to back configuration and cannot interfere with (a).
• Figure 3: 3d Ising model allowed region for $C_{TT\varepsilon}$ and $C_{TT\varepsilon'}$.