Abstract
We consider light-like Wilson loops with hexagonal geometry in the planar limit of N=4 Super-Yang-Mills theory. Within the Operator-Product-Expansion framework these loops receive contributions from all states that can propagate on top of the colour flux tube sourced by any two opposite edges of the loops. Of particular interest are the two-particle contributions. They comprise virtual effects like the propagation of a pair of scalars, fermions, and gluons, on top of the flux tube. Each one of them is thoroughly discussed in this paper. Our main result is the prediction of all the twist-2 corrections to the expansion of the dual 6-gluons MHV amplitude in the near-collinear limit at finite coupling. At weak coupling, our result was recently used by Dixon, Drummond, Duhr and Pennington to predict the full amplitude at four loops. At strong coupling, it allows us to make contact with the classical string description and to recover the (previously elusive) AdS(3) mode from the continuum of two-fermion states. More generally, the two-particle contributions serve as an exemplar for all the multi-particle corrections.
Highlights
In the planar N = 4 Super-Yang-Mills theory, null polygonal Wilson loops can be computed at any value of the coupling using the Operator Product Expansion [1]
In this approach, which is analogous to the usual OPE for local operators, the Wilson loop is decomposed into sums over the color flux-tube eigenstates ψ propagating in the consecutive OPE channels [2]
The associated two contributions both take the form of a single integral (3.2) over the rapidity u. This is nothing but the sum over the momentum p of the gluon that is propagating through the middle square of the hexagon Wilson loop (1.1)
Summary
The simplest example, which will be the focus of this paper, is the hexagonal Wilson loop or, more precisely, the conformally invariant finite ratio W ≡ Whexagon introduced in [3, 4] It is given as a sum over a single OPE channel [3]. The most non-trivial ingredients in this expression are the form factors P (0|ψ) and P (ψ|0) They stand for the creation and annihilation amplitudes of the state ψ at the bottom and top of the hexagon, respectively, and are the Wilson loop analog of the familiar structure constants for correlation functions. Beyond it stands the realm of multi-particle corrections which for the most part is uncharted territory Among all these contributions, those associated to the two-particle states are dominating at large τ , see figure 1, and are the simplest ones. The mass of the f√ermions is protected by supersymmetry [12] while the one of the gluons interpolates between 1 and 2
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