Conformal properties of four-gluon planar amplitudes and Wilson loops

TL;DR

This paper provides evidence for dual conformal symmetry in four-gluon planar amplitudes in N=4 SYM, linking perturbative calculations, Wilson loops, and the Regge limit, revealing deep structural properties of the theory.

Contribution

It demonstrates that all relevant momentum integrals are dual conformal and derives the finite remainder form, connecting weak and strong coupling results and Wilson loop calculations.

Findings

All momentum integrals are dual conformal and well-defined off shell.

The finite remainder matches between weak coupling amplitude and Wilson loop calculations.

The Regge limit of the amplitude coincides with the exact expression for all Mandelstam variables.

Abstract

We present further evidence for a dual conformal symmetry in the four-gluon planar scattering amplitude in N=4 SYM. We show that all the momentum integrals appearing in the perturbative on-shell calculations up to five loops are dual to true conformal integrals, well defined off shell. Assuming that the complete off-shell amplitude has this dual conformal symmetry and using the basic properties of factorization of infrared divergences, we derive the special form of the finite remainder previously found at weak coupling and recently reproduced at strong coupling by AdS/CFT. We show that the same finite term appears in a weak coupling calculation of a Wilson loop whose contour consists of four light-like segments associated with the gluon momenta. We also demonstrate that, due to the special form of the finite remainder, the asymptotic Regge limit of the four-gluon amplitude coincides with the exact expression evaluated for arbitrary values of the Mandelstam variables.