From amplitudes to exact S-matrices

The exact S-matrices for a variety of integrable quantum field theories in two dimensions have been known for many years. These theories can often also be studied perturbatively using standard Feynman diagrams, where the integrability manifests itself in a priori surprising cancellations and simplifications. The project will investigate this phenomenon for the affine Toda field theories, where hints of deeper structure already exist in, for example, the relationship between on-shell diagrams for singularities in amplitudes to planar projections of certain higher-dimensional polytopes. The insights from this project can be used for the computations
of amplitudes as well as the bootstrap for Quantum Field Theories in Anti-de Sitter space.