NLO evolution of color dipoles in N = 4 SYM

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 N = 4 SYM theory. We define the “composite dipole operators” with the rapidity cutoff preserving conformal invariance. The resulting Möbius-invariant kernel for these operators agrees with the forward NLO BFKL calculation of [A.V. Kotikov, L.N. Lipatov, Nucl. Phys. B 582 (2000) 19; A.V. Kotikov, L.N. Lipatov, Nucl. Phys. B 661 (2003) 19; A.V. Kotikov, L.N. Lipatov, Nucl. Phys. B 685 (2004) 405, Erratum].