Resonant resurgent asymptotics from quantum field theory

TL;DR

This paper conducts a comprehensive resurgence analysis of a specific quantum field theory renormalon in six-dimensional scalar $^3$ theory, revealing novel logarithmic features in the trans-series expansion.

Contribution

It introduces a detailed all-order resurgence framework for a renormalon in quantum field theory, including the first explicit account of logarithmic terms in the trans-series.

Findings

Identification of logarithmic terms at second-instanton order

Development of a conjectured formula for all instanton contributions

Analysis of a related differential equation illustrating the resonant structure

Abstract

We perform an all-order resurgence analysis of a quantum field theory renormalon that contributes to an anomalous dimension in six-dimensional scalar $\phi^3$ 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.