Taming a resurgent ultra-violet renormalon

TL;DR

This paper investigates the challenge of controlling ultra-violet renormalons in quantum field theory, specifically in 6-dimensional $^3$ theory, using resurgence techniques to handle divergent perturbative expansions.

Contribution

It provides a high-loop-order analysis of ultra-violet renormalons in $^3$ theory and applies resurgence methods to tame these divergences, advancing understanding of non-perturbative effects.

Findings

High-order loop calculations of the ultra-violet renormalon

Application of resurgence techniques to control divergences

Insights into the complexity of renormalon problems in higher dimensions

Abstract

Perturbative expansions in quantum field theory diverge for at least two reasons: the number of Feynman diagrams increases dramatically with the loop number and the process of renormalization may make the contribution of some diagrams large. We give an example of the second problem, from an ultra-violent renormalon of $\phi^3$ theory in 6 dimensions, where we can compute to very high loop-order. Taming this renormalon involves recent work on resurgence. This challenge is much more demanding than the corresponding problem for Yukawa theory in 4 dimensions.