Title: New formulations of perturbative quantum field theory

Abstract: The S-matrix is among the most basic -- and most physically relevant -- observables in any quantum field theory. At tree-level, it is well-defined even for theories that are not UV finite, such as general relativity, and captures the full non-linear complexity of the equations of motion. The traditional Feynman approach to computing S-matrix elements (scattering amplitudes) relies on a space-time Lagrangian description of the QFT we are interested in. However, remarkably compact expressions have been discovered for the full tree-level S-matrix of a wide array of massless QFTs which have no obvious derivation from standard Feynman rules. I will discuss how such formulae arise from certain two-dimensional conformal field theories.

These 2d models give novel expressions for the S-matrix at higher loop orders (when this is well-defined) and also encode the equations of motion which we would usually think of as arising from a space-time Lagrangian.