The averaged null energy operator (ANEC) is a light-ray integral of the null energy, which is known to have far-reaching consequences in CFT, such as the Lorentzian Inversion Formula. It is also closely connected to modular Hamiltonian in QFT. In this talk, I will discuss a new connection between the ANEC operator and monotonicity of the renormalization group. In particular, I will show how the 2d c-theorem and 4d a-theorem can be derived using the ANEC. This derivation relies on contact terms appearing in specific ANEC correlators. I will also review a new infinite set of constraints that can be derived from the ANEC in 2d QFT. This program hints at a more general role for light-ray operators in QFT, which I will argue for.
