Averaged null energy and the renormalization group

The averaged null energy operator is known to be closely tied to causality, quantum information, and the Regge limit of correlation functions in CFT. I will discuss a new connection between averaged null energy and the monotonicity of the renormalization group, and use the averaged null energy condition (ANEC) to derive the c-theorem in two dimensions and the a-theorem in four dimensions. The derivation is based on contact terms that appear in correlation functions of the null energy operator. Combined with previous results, this also gives a new derivation of the c- and a-theorems from the monotonicity of relative entropy, and hints at a more general role for Lorentzian inversion and light-ray operators in non-conformal QFTs.