Hexagon Wilson loop OPE and Harmonic Polylogarithms

par Georgios Papathanasiou (LAPTh)

jeudi 10 oct. 2013, 14:00 → 15:00 Europe/Paris

Petit Amphithéâtre (Annecy-le-Vieux)

A recent, integrability-based conjecture in the framework of the Operator Product Expansion (OPE) for Wilson loops in N=4 super Yang-Mills theory, predicts the leading OPE contribution for the hexagon Maximally Helicity Violating (MHV) remainder function and Next-to-MHV (NMHV) ratio function to all loops, in integral form. We prove that these integrals evaluate to a particular basis of harmonic polylogarithms, at any order in the weak coupling expansion. The proof constitutes an algorithm for the direct computation of the integrals, which we employ in order to obtain the full (N)MHV OPE contribution in question up to 6 loops, and certain parts of it up to 12 loops. The feasibility of obtaining the first term in the OPE expansion in principle at arbitrary loop order, offers promise for the suitability of this approach as a non-perturbative description of Wilson loops/scattering amplitudes.