The Holographic Fishchain

We present the first-principle derivation of a weak-strong duality between the fishnet theory in four dimensions and a discretized string-like model living in five dimensions. At strong coupling, the dual description becomes classical and we demonstrate explicitly the classical integrability of the model. We test our results by reproducing the strong coupling limit of the $4$-point correlator computed before non-perturbatively from the conformal partial wave expansion. Due to the extreme simplicity of our model, it could provide an ideal playground for holography with no super-symmetry. Furthermore, since the fishnet model and ${\cal N}=4$ SYM theory are continuously linked our consideration could shed light on the derivation of AdS/CFT for the latter.Comment: 5 pages. v2: references added, v3 - acknowledgment adde

Planar scattering amplitudes from Wilson loops

We derive an expression for parton scattering amplitudes of planar gauge theory in terms of sums of Wilson loops. We study in detail the example of Yang-Mills theory with an adjoint Higgs field. The expression exhibits the T-duality performed by Alday and Maldacena in the AdS dual as a Fourier transform in loop space. When combined with the AdS/CFT correspondence for Wilson loops and a strong coupling argument for the dominance of 1PI diagrams, this leads to a derivation of the Alday-Maldacena holographic prescription for scattering amplitudes in terms of momentum Wilson loops. The formula leads to a conjecture for a relationship between position-space and momentum-space Wilson loops in N=4 SYM at finite coupling.Comment: 30 + 16 pages, 9 figures. v2: corrected section

Hexagonal Wilson Loops in Planar N=4\mathcal{N}=4 SYM Theory at Finite Coupling

We report on the complete OPE series for the 6-gluon MHV and NMHV amplitudes in planar $\mathcal{N}=4$ SYM theory. Namely, we provide a finite coupling prediction for all the terms in the expansion of these amplitudes around the collinear limit. These furnish a non-perturbative representation of the full amplitudes.Comment: 2 pages + reference

Space-time S-matrix and Flux-tube S-matrix III. The two-particle contributions

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.Comment: 40 pages + 37 pages of appendices, 24 figures, no footnote

Adjoint BFKL at finite coupling: a short-cut from the collinear limit

In the high energy Regge limit, the six gluons scattering amplitude is controlled by the adjoint BFKL eigenvalue and impact factor. In this paper we determine these two building blocks at any value of the 't Hooft coupling in planar $\cal{N}$=4 SYM theory. This is achieved by means of analytic continuations from the collinear limit, where similar all loops expressions were recently established. We check our predictions against all available data at weak and strong coupling.Comment: 30 pages plus appendices, 12 figures. References added; published versio