Spacetime and Flux Tube<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>S</mml:mi></mml:math>-Matrices at Finite Coupling for<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi mathvariant="bold-script">N</mml:mi><mml:mo>=</mml:mo><mml:mn>4</mml:mn></mml:math>Supersymmetric Yang-Mills Theory

We propose a nonperturbative formulation of planar scattering amplitudes in N=4 supersymmetric Yang-Mills theory, or, equivalently, polygonal Wilson loops. The construction is based on the operator product expansion approach and introduces a new decomposition of the Wilson loop in terms of fundamental building blocks named pentagon transitions. These transitions satisfy a simple relation to the worldsheet S matrix on top of the so-called Gubser-Klebanov-Polyakov vacuum which allows us to bootstrap them at any value of the coupling. In this Letter we present a subsector of the full solution which we call the gluonic part. We match our results with both weak and strong coupling data available in the literature.