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High-energy scattering in pQCD in the Regge limit is described by the evolution of Wilson lines governed by the BK equation. In the leading order, the BK equation is conformally invariant and the eigenfunctions of the linearized BFKL equation are powers. It is a common belief that at $d\neq 4$ the BFKL/BK equation is useless since unlike $d=4$ case it cannot be solved by powers. However, I demonstrate that at critical Wilson-Fisher point of QCD the relevant part of NLO BK restores the conformal invariance so the solutions are again powers. As a check of this approach, I calculate the anomalous dimensions of twist-2 light-ray operators in the BFKL limit.