Characterize additional locality constraints on energy correlators

Determine whether additional universal constraints beyond non-negativity of the two-point energy correlator F(z) and its partial wave coefficients F_l are required to ensure that F(z) arises from a local quantum field theory, and establish whether the resulting bounds on F_l can be saturated by energy correlators in physical theories.

Background

The paper defines the EEC-hedron by imposing non-negativity of the two-point energy correlator F(z) and of all partial wave coefficients F_l. These assumptions yield rigorous bounded regions for the allowed coefficients, but they are not shown to be sufficient for an energy correlator to have a realization in a local quantum field theory.

The unresolved issue is whether locality and other structural properties of quantum field theory impose further universal restrictions. If such restrictions exist, the EEC-hedron would be strictly larger than the physically realizable region, whereas saturation by actual theories—potentially free theories—would suggest that positivity captures the complete set of universal constraints.

References

However, it is unclear what (if any) additional constraints must be imposed on $F(z)$ to ensure it arises from a local QFT. In other words, are the bounds we have computed on $F_\ell$ saturated by energy correlators in physical theories, or are there additional universal constraints that will further reduce the allowed region?

— 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”