High Energy Theory Seminar

Renormalized perturbation theory for QFTs typically produces divergent series, even when the coupling constant is small, because the series coefficients grow factorially at high order. So in what sense do such divergent series capture the physics of QFTs? The question is not purely formal because the worst divergences in asymptotically-free theories like QCD, known as renormalons, were conjectured by ’t Hooft to be related to confinement and the mass gap, but making the connection precise has been very challenging. I will discuss a recent conjecture that the semiclassical expansion of path integrals for asymptotically free QFTs - roughly, perturbation theory - yields well-defined answers once the implications of resurgence theory are taken into account. Resurgence theory relates expansions around different saddle points of a path integral to each other, and has the striking practical implication that the high-order divergences of perturbative series encode precise information about the non-perturbative physics of a theory and vice versa. These ideas will be discussed in the context of a QCD-like toy model theory, the two-dimensional principal chiral model, where resurgence theory appears to be capable of dealing with renormalons. Fitting ’t Hooft’s conjecture, understanding the origin of renormalon divergences allows us to see the microscopic origin of the mass gap of the theory in the semiclassical domain.