Renormalon's Contribution to Effective Couplings

TL;DR

This paper explores how ultraviolet renormalons contribute non-perturbative effects to effective couplings and operators in theories with mass parameters, using the O(N) symmetric $^4$ model and comparing with Seiberg-Witten theory.

Contribution

It demonstrates the role of UV renormalons in generating non-perturbative contributions in non-asymptotically free theories, highlighting their similarity to instanton effects.

Findings

UV renormalons induce non-perturbative effects in effective couplings.

The effect is illustrated in the O(N) $^4$ model using the $1/N$ expansion.

Comparison made with non-perturbative corrections in Seiberg-Witten theory.

Abstract

When an asymptotically non-free theory possesses a mass parameter, the ultraviolet (UV) renormalon gives rise to non-perturbative contributions to dimension-four operators and dimensionless couplings, thus has a similar effect as the instanton. We illustrate this phenomenon in O(N) symmetric massive $\lambda\phi^4$ model in the $1/N$ expansion. This effect of UV renormalon is briefly compared with non-perturbative corrections in the magnetic picture of the Seiberg-Witten theory.