RG flows and resonance scattering amplitudes

We review recent progresses in the study of factorized resonance scattering S-matrices. The resonance amplitudes are introduced through a suitable analytical continuation of the ADE Toda S-matrices. By using the thermodynamic Bethe ansatz approach we are able to compute the ground state energy, which describes a rich pattern of flows interpolating between the central charges of the coset models based on the ADE Lie algebras. We also present the simplest resonance ``$\phi^3$'' scattering model and discuss its relation with new flows in non-unitary minimal models. Further generalizations are discussed in terms of certain asymptotic conditions in a family of ``resonance'' functional hierarchies.