Speaker: Prof. Marcos Mariño* (University of Geneva, Switzerland)*

Recording: https://vimeo.com/608501824

Title: Resurgence and renormalons in quantum field theory

Abstract:

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 including renormalon

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 including renormalon

corrections, and I will discuss more generally the virtues and limits of the resurgent approach.