English

Resonant resurgent asymptotics from quantum field theory

High Energy Physics - Theory 2022-06-16 v2 Mathematical Physics Classical Analysis and ODEs math.MP

Abstract

We perform an all-order resurgence analysis of a quantum field theory renormalon that contributes to an anomalous dimension in six-dimensional scalar ϕ3\phi^3 theory and is governed by a third-order 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 well-tested formula. A distinctive feature of this renormalon singularity is the appearance of logarithmic terms, starting at second-instanton order in the trans-series. To highlight this and to illustrate our methods, we also analyze the trans-series for a closely related second-order nonlinear differential equation that exhibits a similarly resonant structure but lacks logarithmic contributions.

Keywords

Cite

@article{arxiv.2202.01513,
  title  = {Resonant resurgent asymptotics from quantum field theory},
  author = {Michael Borinsky and David Broadhurst},
  journal= {arXiv preprint arXiv:2202.01513},
  year   = {2022}
}

Comments

34 pages, v2: Discussion on ODE ambiguities and typos corrected. Accepted version to appear in Nuclear Physics B

R2 v1 2026-06-24T09:17:32.545Z