Resonant resurgent asymptotics from quantum field theory
Abstract
We perform an allorder resurgence analysis of a quantum field theory renormalon that contributes to an anomalous dimension in sixdimensional scalar ϕ^{3} theory and is governed by a thirdorder nonlinear differential equation. We augment the factorially divergent perturbative expansion associated to the renormalon by asymptotic expansions to all instanton orders, in a conjectured and welltested formula. A distinctive feature of this renormalon singularity is the appearance of logarithmic terms, starting at secondinstanton order in the transseries. To highlight this and to illustrate our methods, we also analyze the transseries for a closely related secondorder nonlinear differential equation that exhibits a similarly resonant structure but lacks logarithmic contributions.
 Publication:

Nuclear Physics B
 Pub Date:
 August 2022
 DOI:
 10.1016/j.nuclphysb.2022.115861
 arXiv:
 arXiv:2202.01513
 Bibcode:
 2022NuPhB.98115861B
 Keywords:

 High Energy Physics  Theory;
 Mathematical Physics;
 Mathematics  Classical Analysis and ODEs
 EPrint:
 34 pages, v2: Discussion on ODE ambiguities and typos corrected. Accepted version to appear in Nuclear Physics B