Lecturer: Dr. Aleksey Cherman
Affiliation: University of Minnesota
Abstract:
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.
Additional details of the upcoming Joint Seminars
in Theoretical High Energy Physics can be found
on the following link