Abstract

The factorial divergence of perturbative expansions is believed to be governed by two seemingly unrelated phenomena: Instantons that arise due to nontrivial solutions of the classical field equations and renormalons that appear due to a factorially growing contribution from the renormalization subtraction terms of a family of Feynman diagrams.  I will report on joint work with David Broadhurst, Gerald Dunne and Max Meynig in which a particularly interesting renormalon in phi^3 theory was analyzed using tools from Ecalle’s resurgence framework. A recent work with David Broadhurst revealed the intricate role of ‘resonant’ logarithmic terms for this renormalon and allowed an all-trans-series-order resurgence analysis. The overall shape of our all-order trans-series solution and our (well-tested) conjectured formulas for the asymptotic behaviour of the trans-series coefficients hint at the existence of a reality cancellation mechanism as it is observed in quantum mechanical instanton computations. (Based on https://arxiv.org/abs/2202.01513 )