Hexagon Wilson loop = six-gluon MHV amplitude

TL;DR

This paper provides evidence that the duality between Wilson loops and scattering amplitudes in planar N=4 SYM theory holds at all loops for any number of particles, by comparing two-loop corrections to hexagon Wilson loops and six-gluon amplitudes.

Contribution

It demonstrates the equivalence of two-loop corrections to the hexagon Wilson loop and six-gluon MHV amplitude, supporting the all-loop Wilson loop/scattering amplitude duality in N=4 SYM.

Findings

Two-loop corrections match within error bars.

Deviations from BDS ansatz are captured by a non-trivial function.

Supports duality conjecture in planar N=4 SYM.

Abstract

We compare the two-loop corrections to the finite part of the light-like hexagon Wilson loop with the recent numerical results for the finite part of the MHV six-gluon amplitude in N=4 SYM theory by Bern, Dixon, Kosower, Roiban, Spradlin, Vergu and Volovich (arXiv:0803.1465 [hep-th]) and demonstrate that they coincide within the error bars and, at the same time, they differ from the BDS ansatz by a non-trivial function of (dual) conformal kinematical invariants. This provides strong evidence that the Wilson loop/scattering amplitude duality holds in planar N=4 SYM theory to all loops for an arbitrary number of external particles.