High-energy evolution to three loops

TL;DR

This paper derives the three-loop corrections to the Balitsky-Kovchegov equation in planar N=4 super Yang-Mills theory, linking high-energy evolution with non-global logarithms and developing a Lorentz-covariant divergence subtraction method.

Contribution

It provides the first three-loop evolution equation for high-energy scattering in N=4 SYM and connects it with non-global logarithms, also introducing a new divergence subtraction technique.

Findings

Three-loop correction to the BK equation obtained.

Established equivalence with non-global logarithms.

Developed a Lorentz-covariant divergence subtraction method.

Abstract

The Balitsky-Kovchegov equation describes the high-energy growth of gauge theory scattering amplitudes as well as nonlinear saturation effects which stop it. We obtain the three-loop corrections to this equation in planar $\mathcal{N}=4$ super Yang-Mills theory. Our method exploits a recently established equivalence with the physics of soft wide-angle radiation, so-called non-global logarithms, and thus yields at the same time the three-loop evolution equation for non-global logarithms. As a by-product of our analysis, we develop a Lorentz-covariant method to subtract infrared and collinear divergences in cross-section calculations in the planar limit. We compare our result in the linear regime with a recent prediction for the so-called Pomeron trajectory, and compare its collinear limit with predictions from the spectrum of twist-two operators.