Evolution equations beyond one loop from conformal symmetry

Understand

We study implications of exact conformal invariance of scalar quantum field theories at the critical point in non-integer dimensions for the evolution kernels of the light-ray operators in physical (integer) dimensions.

• We demonstrate that all constraints due the conformal symmetry are encoded in the form of the generators of the collinear sl(2) subgroup.
• Two of them, S_- and S_0, can be fixed at all loops in terms of the evolution kernel, while the generator of special conformal transformations, S_+, receives nontrivial corrections which can be calculated order by order in perturbation theory.
• Provided that the generator S_+ is known at the k-1 loop order, one can fix the evolution kernel in physical dimension to the k-loop accuracy up to terms that are invariant with respect to the tree-level generators.