Determine additional consistency conditions for conformal field theories

Determine the additional constraints beyond vanishing of F_1 that are required for the partial wave coefficients of an energy correlator to be consistent with fundamental properties of conformal field theories, including conformal invariance and convergence of the operator-product expansion.

Background

For conformal field theories, the paper supplements positivity and unitarity with the momentum-conservation condition F_1=0. The authors argue that this condition is unlikely to exhaust the restrictions imposed by conformal field theory.

The unresolved task is to identify further constraints associated with conformal invariance and convergence of the operator-product expansion, with the aim of sharpening the EEC-hedron and improving the resulting bounds on stress-tensor OPE coefficients.

References

It seems very likely, however, that additional constraints need to be imposed to ensure consistency with fundamental properties of CFTs, such as conformal invariance and convergence of the OPE. It would be exciting to determine these additional constraints and potentially further improve the bounds on OPE coefficients computed in this work.

— The EEC-Hedron: Positivity Bounds on Energy Correlators  (2608.19322 - Meçaj et al., 19 Aug 2026) in Section Discussion, subsection “Additional constraints for physical theories”