From Symmetries to Geometry and Beyond: a Modern Approach to Scattering Amplitudes

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The goal of this project is to provide significant steps towards a modern approach to Quantum Field Theories (QFT), especially through a novel understanding of scattering amplitudes.QFT is among the most successful mathematical frameworks in physics. Its traditional starting point is a Lagrangian: the Feynman rules derived from it allow to compute perturbatively physical quantities. Among these, a prominent role is played by scattering amplitudes, describing the interactions between particles. Standard Feynman computations have made possible tremendous progress in giving theoretical predictions for amplitudes of direct relevance for experiments at high-energy colliders. There is, however, strong evidence that more fundamental, underlying principles have yet to be discovered. A significant indication of a missing principle is the remarkable simplicity of final results for amplitudes, despite the complexity of intermediate computations in the traditional Feynman expansion. This is very evident in exactly solvable QFTs, such as planar maximally supersymmetric Yang-Mills theory, where novel insights for amplitudes and for the theories themselves are provided by, for instance, emergent infinite dimensional symmetries and are not manifest from a standard Feynman approach. Furthermore, new geometric formulations for amplitudes have been proposed, which are far away from any traditional presentation as possible. The standard foundations of QFTs, such as unitarity and locality, are not manifest but rather emerge naturally. Investigations of symmetries and fundamental, geometric properties have made possible developments not accessible from a Lagrangian point of view. This project explores these fascinating questions and is aimed at analysing the remarkable properties of maximally supersymmetric Yang-Mills theory, focusing on its symmetries, new computational technologies and fundamental insights based on the geometrization of amplitudes. This offers the basics for a novel point of view on gravity theories and Quantum Chromodynamics.