Resurgent structure of the 't Hooft-Polyakov monopole

TL;DR

This paper applies resurgence theory to analyze the differential equations of the 't Hooft-Polyakov monopole, revealing universal non-perturbative profiles and providing a detailed understanding of the solutions' asymptotics.

Contribution

It introduces a resurgence-based framework to study monopole solutions, uncovering universal analytic non-perturbative backgrounds and controlling singularities at all orders.

Findings

Universal asymptotic behavior of gauge components.

Explicit non-perturbative background profiles.

Controlled Borel-plane singularities and logarithmic discontinuities.

Abstract

In this letter we present a comprehensive analysis of the differential equations governing the spatial profile of the 't~Hooft-Polyakov monopole from the viewpoint of resurgence theory. We note that the universality of the gauge-component asymptotics, together with the relative simplicity of its Borel transform and the associated Volterra equations' kernels, gives rise to a perturbative expansion featuring a good control over the proliferation of the Borel-plane singularities to all orders, along with full information about the relevant logarithmic discontinuities. Moreover, its partial resummation reveals remarkably simple universal analytic non-perturbative background profiles, around which one can develop a uniformly convergent global perturbative expansion of the exact solutions for any $\lambda/e^2>0$. This also provides an analytic grip on the numerical parameters governing the expansions of both the gauge and scalar profile functions at the origin and at infinity.