Speaker
Description
Understanding the behavior of perturbative series in quantum field theory is an old
and venerable problem. In the 1970s-1980s it was found that this behavior is closely connected to non-perturbative physics, and ’t Hooft and Parisi argued that the most important non-perturbative corrections in asymptotically free theories are due to renormalons. In contrast to instantons, renormalons do not have a semi-classical description, they are difficult to compute, and they are still poorly understood. In this talk I will show that integrable, asymptotically free field theories in two dimensions provide an excellent laboratory to study renormalons. In particular, one can obtain for the first time analytic results on their structure at finite N, which turn out to challenge the standard orthodoxy on the subject. Our results also provide exact, testable trans-series representations of physical observables, i.e. extensions of perturbative series which include exponentially small corrections, as expected from the theory of resurgence.
