The light-ray OPE and conformal colliders

We derive a nonperturbative, convergent operator product expansion (OPE) for null-integrated operators on the same null plane in a CFT. The objects appearing in the expansion are light-ray operators, whose matrix elements can be computed by the generalized Lorentzian inversion formula. For example, a product of average null energy (ANEC) operators has an expansion in the light-ray operators that appear in the stress-tensor OPE. An important application is to collider event shapes. The light-ray OPE gives a nonperturbative expansion for event shapes in special functions that we call celestial blocks. As an example, we apply the celestial block expansion to energy-energy correlators in N = 4 Super Yang-Mills theory. Using known OPE data, we find perfect agreement with previous results both at weak and strong coupling, and make new predictions at weak coupling through 4 loops (NNNLO).

Automated summary

The study introduces a nonperturbative, convergent operator product expansion (OPE) for dealing with null-integrated operators on the same null plane in a conformal field theory. The objects in the expansion are light-ray operators, which can be computed using the generalized Lorentzian inversion formula. An application of this is in collider event shapes, where the light-ray OPE provides a nonperturbative expansion for event shapes in celestial blocks.