Resumming perturbative series in the presence of monopole bubbling effects

Monopole bubbling effect is screening of magnetic charges of singular Dirac monopoles by regular 't Hooft-Polyakov monopoles. We study properties of weak coupling perturbative series in the presence of monopole bubbling effects as well as instantons. For this purpose, we analyze supersymmetric 't Hooft loop in four dimensional $\mathcal{N}=2$ supersymmetric gauge theories with Lagrangians and non-positive beta functions. We show that the perturbative series of the 't Hooft loop is Borel summable along positive real axis for fixed instanton numbers and screened magnetic charges. It turns out that the exact result of the 't Hooft loop is the same as the sum of the Borel resummations over instanton numbers and effective magnetic charges. We also obtain the same result for supersymmetric dyonic loops.