Chaos on the mass shell

Abstract

We study particle production in high-energy states for theories given by an RG flow between an asymptotically free or conformal theory in the UV and a massive theory in the IR. Using the framework of detector matching, we argue that distributions of produced particles satisfy universal evolution equations with energy, determined by the spectrum of light-ray operators of the UV theory. In particular, we interpret the UV Chew-Frautschi plot as a wave equation for particle densities on the mass shell, evolving with energy. (When the UV theory is a CFT, this wave equation is the same one that controls the spread of chaos in hyperbolic space at a particular temperature.) We test these ideas for integrable flows in 2d CFTs, finding an independent derivation of the evolution equations in terms of the thermodynamics of a Feynman gas. We also discuss consequences for 4d gauge theories, including the presence of a BFKL contrail produced by an outgoing wave of hadron number density.