IR divergences and Regge limits of subleading-color contributions to the four-gluon amplitude in N=4 SYM Theory

TL;DR

This paper derives a comprehensive all-loop expression for IR divergences in four-gluon amplitudes in N=4 SYM, including subleading-color effects, and analyzes their Regge behavior, revealing less severe growth and complex trajectory structures.

Contribution

It provides the first all-loop-order formula for IR divergences including subleading-color contributions in N=4 SYM and explores their Regge limit behavior.

Findings

Subleading-color amplitudes grow less rapidly in the Regge limit than planar ones.

Double-trace amplitudes exhibit Regge cuts starting at three loops.

The Regge trajectories for non-planar contributions are complex and differ from planar cases.

Abstract

We derive a compact all-loop-order expression for the IR-divergent part of the N=4 SYM four-gluon amplitude, which includes both planar and all subleading-color contributions, based on the assumption that the higher-loop soft anomalous dimension matrices are proportional to the one-loop soft anomalous dimension matrix, as has been recently conjectured. We also consider the Regge limit of the four-gluon amplitude, and we present evidence that the leading logarithmic growth of the subleading-color amplitudes is less severe than that of the planar amplitudes. We examine possible 1/N^2 corrections to the gluon Regge trajectory, previously obtained in the planar limit from the BDS ansatz. The double-trace amplitudes have Regge behavior as well, with a nonsense-choosing Regge trajectory and a Regge cut which first emerges at three loops.