S-matrix bootstrap and non-invertible symmetries

We initiate the S-matrix bootstrap analysis of theories with non-invertible symmetries in (1+1) dimensions. Our previous work [1] showed that crossing symmetry of S-matrices in such theories is modified, with modification characterized by the fusion categorydata. By imposing unitarity, symmetry and the modified crossing, we constrain the space o fconsistent S-matrices, identifying integrable theories with non-invertible symmetries at the cusps of allowed regions. We also extend the modified crossing rules to cases where vacuatransform in non-regular representations of fusion category, utilizing a connection to a dual categoryC & lowast;Mand Symmetry Topological Field Theory (SymTFT). This highlights the utilityof SymTFT in the analysis of scattering amplitudes