Lightcone Conformal Truncation and the S-matrix Bootstrap, Together at Last

A compelling view of Quantum Field Theories (QFTs) is that they are points along the RG flow between fixed points described by Conformal Field Theories (CFTs), which in turn are fully characterized by a discrete set of "CFT data". In this talk, we describe how this picture can be turned into a useful calculational tool for studying QFT at strong coupling by applying a variational method motivated by the conformal structure of the ultraviolet CFT fixed point of the theory. We describe how combining this method with the S-matrix bootstrap, and a recent generalization of it that involves spectral densities and form factors, one can efficiently extract precise scattering amplitudes in 2d phi^4 theory for couplings that range from the perturbative regime up to near the critical point.