One-cycle negative geometries in N=4 SYM have singularities only at z=-1, 0, and infinity to all loop orders.
Space-time S-matrix and Flux-tube S-matrix III. The two-particle contributions
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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.
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The chiral algebra bootstrap yields all-loop splitting functions for self-dual N=4 SYM, a proof of no double-pole OPEs, and novel two-loop form factors with anti-self-dual field strength insertions.
In planar N=4 SYM the IR-finite hard amplitude satisfies an uncorrected tree-level soft theorem and represents the undeformed tree-level S-algebra of soft gluons.
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Landau Analysis of One-Cycle Negative Geometries
One-cycle negative geometries in N=4 SYM have singularities only at z=-1, 0, and infinity to all loop orders.
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Soft Algebra for ${\cal N}=4$ SYM
In planar N=4 SYM the IR-finite hard amplitude satisfies an uncorrected tree-level soft theorem and represents the undeformed tree-level S-algebra of soft gluons.