Small-x Evolution in the Next-to-Leading Order

The high-energy behavior of amplitudes in gauge theories can be reformulated in terms of the evolution of Wilson-line operators. In the leading order this evolution is governed by the non-linear BK equation. The NLO corrections define the scale of the running-coupling constant in the BK equation and in QCD, its kernel has both conformal and non-conformal parts. 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, then we define the 'composite dipole operator' with the rapidity cutoff preserving conformal invariance, and the resulting Moebius invariant kernel for this operator agrees with the forward NLO BFKL calculation.