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We present the first numerical solution to the next to leading orderBalitsky-Kovchegov (BK) equation in coordinate space in thelarge-$N_\mathrm{c}$ limit. In addition to the dipole operator we also solvethe evolution of the "conformal dipole" for which the conformal invariancebreaking double logarithmic term is absent from the evolution equation. The NLOcorrections are shown to slow down the evolution. We show that the solutiondepends strongly on the details of the initial condition, and that the solutionto the equation is not positive definite with all initial conditions relevantfor phenomenological applications.

Direct numerical solution of the coordinate space Balitsky-Kovchegov equation at next to leading order