The EEC-Hedron: Positivity Bounds on Energy Correlators

We study the constraints placed by energy positivity on general unitary quantum field theories. We show that the coefficients in the partial wave expansion of energy-energy correlators all must lie within a bounded region of parameter space, which we call the ``EEC-hedron’'. For the particular case of conformal field theories, these positivity constraints on energy correlators lead to bounds on the allowed values of coefficients in the operator product expansion. We demonstrate this approach in the 3d Ising and $O(2)$ CFTs, deriving new bounds on OPE coefficients in both theories.