High-energy amplitudes in the next-to-leading order

TL;DR

The work develops a rapidity-factorized high-energy operator expansion in Wilson lines to compute next-to-leading order amplitudes in gauge theories. It applies this framework to ${\cal N}=4$ SYM where conformal invariance allows a conformal dipole formalism and explicit NLO Pomeron results, and to QCD where running coupling introduces nonconformal contributions, requiring a composite dipole to preserve invariance at NLO. A central achievement is the explicit construction of the NLO BK kernel and the NLO scattering amplitude, including the conformal dipole evolution and the NLO pomeron residue, with consistency checks against NLO BFKL in QCD. The approach provides a systematic, symmetry-guided path to high-energy amplitudes at NLO and offers a clear route to improved small-x phenomenology and deeper insights into conformal structure in gauge theories.

Abstract

I review the calculation of the next-to-leading order behavior of high-energy amplitudes in N=4 SYM and QCD using the operator expansion in Wilson lines.

Figures (9)

• Figure 1: Operator product expansion near the light cone. Gauge link is denoted by a dotted line.
• Figure 2: High-energy operator expansion in Wilson lines
• Figure 3: Propagator in a shock-wave background
• Figure 4: Impact factor in the leading order.
• Figure 5: Leading-order diagrams for the small-$x$ evolution of color dipole. Gauge links are denoted by dotted lines.