Speaker
Description
Under certain assumptions and independent of the instantons, we show that the
logarithm expansion of dimensional regularization in quantum field theory needs a
nonperturbative completion to have a renormalization-group flow valid at all ener-
gies. Then, we show that such nonperturbative completion has the analytic proper-
ties of the renormalons, which we find with no reference to diagrammatic calcula-
tions. We demonstrate that renormalon corrections necessarily lead to analyzable
functions, namely, resurgent transseries. A detailed analysis of the resurgent prop-
erties of the renormalons is provided. The self-consistency of the theory requires
these nonperturbative contributions to render the running coupling well-defined at
any energy, thus with no Landau pole. We illustrate the point within the case of
QED. This way, we explicitly realize the correspondence between the nonpertur-
bative Landau pole scale and the renormalons. What is seen as a Landau pole in
perturbation theory is cured by the nonperturbative, resurgent contributions.
