Conformal BK equation at QCD Wilson-Fisher point

TL;DR

This paper demonstrates that at the Wilson-Fisher critical point in QCD, the NLO BK equation regains conformal invariance, allowing solutions similar to the leading order, and calculates related anomalous dimensions in the Regge limit.

Contribution

It shows that the NLO BK equation at the Wilson-Fisher point restores conformal invariance, enabling power-like solutions and providing new insights into high-energy QCD amplitudes.

Findings

NLO BK equation regains conformal invariance at the Wilson-Fisher point

Solutions to the linearized BFKL are powers at this point

Calculated anomalous dimensions of twist-2 operators in the Regge limit

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 $j\rightarrow 1$.}