Non-perturbative corrections to line defect integrated correlators in $Sp(N)$ SCFTs

We consider the $\mathcal{N}=4$ SYM theory with gauge group $Sp(N)$ and the $\mathcal{N}=2$ superconformal field theory consisting of four hypermultiplets in the fundamental representation and one hypermultiplet in the rank-two antisymmetric representation of the $Sp(N)$ gauge group. Building on previous results obtained via supersymmetric localization and a Toda equation, we determine the leading non-perturbative corrections at strong coupling to the integrated correlator between a Wilson line and two Higgs-branch moment map operators. In the case of the $\mathcal{N}=2$ SCFT, the presence of truncated asymptotic expansions led us to develop a resurgent method complementary to Cheshire cat resurgence. This approach has the advantage of yielding an exact expression for the correlator in terms of an analytic function, which can subsequently be expanded in the strong-coupling regime.