NLO evolution of color dipoles in N=4 SYM

TL;DR

This paper computes the next-to-leading order evolution of color dipoles in N=4 supersymmetric Yang-Mills theory, isolating conformal effects and aligning with known BFKL results, advancing understanding of high-energy gauge theory amplitudes.

Contribution

It provides the NLO evolution equation for conformal Wilson-line operators in N=4 SYM, separating conformal and non-conformal effects, and introduces composite operators preserving conformal invariance.

Findings

Derived M"obius invariant kernel for N=4 SYM dipoles.

Confirmed agreement with forward NLO BFKL calculations.

Separated conformal effects from running coupling contributions.

Abstract

High-energy behavior of amplitudes in a gauge theory can be reformulated in terms of the evolution of Wilson-line operators. In the leading logarithmic approximation it is given by the conformally invariant BK equation for the evolution of color dipoles. In QCD, the next-to-leading order BK equation has both conformal and non-conformal parts, the latter providing the running of the coupling constant. To separate the conformally invariant effects from the running-coupling effects, we calculate the NLO evolution of the color dipoles in the conformal ${\cal N}$=4 SYM theory. We define the "composite dipole operators" with the rapidity cutoff preserving conformal invariance. The resulting M\"obius invariant kernel for these operators agrees with the forward NLO BFKL calculation of Ref. 1.