S-matrix bootstrap: Supersymmetry, Z2, and Z4 symmetry

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.