Conformal BK equation at QCD Wilson-Fisher point

Abstract: 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 equation is useless since unlike $d=4$ case it cannot be solved by usual methods. However, we 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 our approach to high-energy amplitudes at the Wilson-Fisher point, we calculate the anomalous dimensions of twist-2 light-ray operators in the Regge limit $j\rightarrow 1$.}