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arXiv · 2602.14620

Resurgent structure of the 't Hooft-Polyakov monopole

Michal Malinský
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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 $λ/e^2>0$. 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.

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Michal Malinský. 2026-05-18. Resurgent structure of the 't Hooft-Polyakov monopole. https://arxiv.org/abs/2602.14620

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