In the past decades, the Standard Model has been established to increasingly higher accuracy at experiments, which is a remarkable achievement for perturbation theory of both the strong and weak interactions. In contrast, tests for nonperturbative predictions of Standard Model physics are sorely lacking, even though nonperturbative phenomena lie at the heart of many expectations for SM and BSM physics. In particular, the role of EW sphalerons in baryogenesis, the role of QCD instantons in strong CP, and the fundamental mass gap problem of Yang-Mills theory are all commonly shared expectations about the behavior of SM physics beyond perturbation theory.
In this vein, the development of effective methods for nonperturbative calculations has a twofold role. First, nonperturbative calculations inherently predict novel and spectacular phenomena outside the realm of perturbative physics, including the production of "soft bombs" or other topological objects at collider energies. Second, the study of the mathematics of nonperturbative computations is an alternative path to making sense of the asymptotic nature of perturbative physics, a connection guaranteed by S-matrix unitarity.
This program aims to review recent progress and open new directions in the understanding of nonperturbative physics. We plan to cover nonperturbative physics in both the SM and also BSM models in the first week, while the second half of the program will discuss the "resurgence" paradigm as well as recent exact results in non-supersymmetric gauge theories. The dedicated study of nonperturbative physics in these contexts will advance our fundamental understanding of quantum field theories.