Resurgent structure of the ’t Hooft-Polyakov monopole

In this paper, 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 useful information about their structure. Moreover, its partial resummation reveals remarkably simple universal analytic “dressed” background, around which one may develop a global perturbative expansion of the exact solutions for any λ / e 2 > 0 and, at least in principle, get a grip on the numerical parameters governing the local expansions of the profile functions.