We consider the 2D S-matrix bootstrap in the presence of supersymmetry, Z 2 , and Z 4 symmetry. At the boundary of the allowed S-matrix space we encounter well-known integrable models such as the supersymmetric sine-Gordon and restricted sine-Gordon models, novel elliptic deformations thereof, as well as a two parameter family of Z 4 elliptic S-matrices previously proposed by Zamolodchikov. We highlight an intricate web of relations between these various S-matrices.

In planar maximally supersymmetric Yang-Mills, we can compute three-point functions at weak coupling using the so-called hexagonalization formalism. The main objects in this framework are called hexagons. We are interested in two sectors of the theory, spanned by operators built entirely from scalar fields, and by spinning operators, respectively. By reviewing the analytic properties of these building blocks, we find new representations for them at weak coupling where the two sectors are on equal footing. We compute the classical limit of the hexagons and of correlation functions in both sectors for some choices of polarizations and our results match previous predictions in the literature.

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