Perturbation theory remains the most general approach to understanding generic quantum theories. However, the series obtained in this way are usually divergent and need to be complemented by additional, non-perturbative information. The theory of resurgence is a framework to make sense of divergent series by using resummation techniques and including non-perturbative information in the form of “trans-series. In quantum mechanics, many observables can be fully understood by using the theory of resurgence, but quantum field theories are more challenging. In realistic quantum field theories, the main source of non-perturbative corrections to the perturbative series are the so-called renormalons, which remain mysterious objects. In this talk I will present the basics of the theory of resurgence and some successful applications in quantum mechanics. I will then move to quantum field theories. In order to address the problems due to renormalons, I will focus on integrable, asymptotically free theories in two dimensions where one can make very explicit analysis. I will show in concrete examples that observables can be computed by trans-series due to renormalons, and I will discuss more generally the virtues and limits of the resurgent approach.
About the spearker
Prof. Marcos Marino is a renowned theoretical physicist from the University of Geneva. He has a wide range of research interests, including string theory, matrix models, Chern-Simons theories, integrable systems, non-perturbative effects in physics, and etc. Recently he is interested in studying non-perturbative effects in quantum mechanics, quantum field theories, and integrable systems, using the resurgence theory.