Duality between Wilson loops and gluon amplitudes

TL;DR

This paper investigates a duality between gluon amplitudes and Wilson loops in N=4 super Yang-Mills, performing two-loop calculations and analyzing conformal Ward identities to test the duality's validity.

Contribution

It extends previous checks of the duality by calculating two-loop Wilson loops and deriving an all-order Ward identity, revealing the duality's agreement with recent numerical results.

Findings

Two-loop calculations support the duality.

The Ward identity constrains Wilson loop functions.

Numerical comparison confirms the duality's validity.

Abstract

An intriguing new duality between planar MHV gluon amplitudes and light-like Wilson loops in N=4 super Yang-Mills is investigated. We extend previous checks of the duality by performing a two-loop calculation of the rectangular and pentagonal Wilson loop. Furthermore, we derive an all-order broken conformal Ward identity for the Wilson loops and analyse its consequences. Starting from six points, the Ward identity allows for an arbitrary function of conformal invariants to appear in the expression for the Wilson loop. We compute this function at six points and two loops and discuss its implications for the corresponding gluon amplitude. It is found that the duality disagrees with a conjecture for the gluon amplitudes by Bern et al. A recent calculation by Bern et al indeed shows that the latter conjecture breaks down at six gluons and at two loops. By doing a numerical comparison with their results we find that the duality between gluon amplitudes and Wilson loops is preserved. This review is based on the author's PhD thesis and includes developments until May 2008.