Integrated Calendar

Renormalized perturbation theory for QFTs typically produces divergent series, because the series coefficients grow factorially at high order. It has been a historical challenge to understand the asymptotic nature of perturbative series, and it has been unclear in what precise sense semiclassical expansions capture the physics of even weakly-coupled QFTs. I will discuss a recent conjecture that the semiclassical expansion of path integrals for asymptotically free QFTs 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 QFT. These ideas will be discussed in the context of several QCD-like theories, where systematic semiclassical control over the dynamics is achieved using adiabatic compactifications on a circle. Fitting a conjecture by ’t Hooft, understanding the origin of the notorious renormalon divergences of perturbation theory of asymptotically-free QFTs allows us to see the microscopic origin of the mass gap of these QFTs in the semiclassical domain.