High-energy amplitudes in N=4 SYM in the next-to-leading order

TL;DR

The paper develops a rapidity-factorized high-energy OPE in Wilson lines for ${\cal N}=4$ SYM and constructs a composite conformal dipole to preserve conformal invariance at NLO. It then computes the NLO amplitude by projecting onto conformal BFKL eigenfunctions and derives the explicit NLO pomeron residue $F(\nu)$, including the function $\Phi_1(\nu)$ and the LO baseline. The approach demonstrates that the high-energy OPE remains valid at NLO and provides a concrete framework for extending these methods to QCD, including photon-structure-function calculations at small $x$. This work thus links the Regge-limit dynamics to a controllable operator expansion in a conformal gauge theory, offering a path toward precision small-$x$ predictions.

Abstract

The high-energy behavior of the N=4 SYM amplitudes in the Regge limit can be calculated order by order in perturbation theory using the high-energy operator expansion in Wilson lines. At large $N_c$, a typical four-point amplitude is determined by a single BFKL pomeron. The conformal structure of the four-point amplitude is fixed in terms of two functions: pomeron intercept and the coefficient function in front of the pomeron (the product of two residues). The pomeron intercept is universal while the coefficient function depends on the correlator in question. The intercept is known in the first two orders in coupling constant: BFKL intercept and NLO BFKL intercept calculated in Ref. 1. As an example of using the Wilson-line OPE, we calculate the coefficient function in front of the pomeron for the correlator of four $Z^2$ currents in the first two orders in perturbation theory.

Figures (2)

• Figure 1: High-energy factorization
• Figure 2: High-energy operator expansion in Wilson lines