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 category data. By imposing unitarity, symmetry and the modified crossing, we constrain the space of consistent 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 vacua transform in non-regular representations of fusion category, utilizing a connection to a dual category \( {\mathcal{C}}_{\mathcal{M}}^{\ast } \) and Symmetry Topological Field Theory (SymTFT). This highlights the utility of SymTFT in the analysis of scattering amplitudes.