Strong coupling expansion of free energy and BPS Wilson loop in $mathcal N=2$ superconformal models with fundamental hypermultiplets

As a continuation of the study (in arXiv:2102.07696 and arXiv:2104.12625) of strong-coupling expansion of non-planar corrections in $mathcal N=2$ 4d superconformal models we consider two special theories with gauge groups $SU(N)$ and $Sp(2N)$. They contain $N$-independent numbers of hypermultiplets in rank 2 antisymmetric and fundamental representations and are planar-equivalent to the corresponding $mathcal N=4$ SYM theories. These $mathcal N=2$ theories can be realised on a system of $N$ D3-branes with a finite number of D7-branes and O7-plane; the dual string theories should be particular orientifolds of $AdS_5times S^5$ superstring. Starting with the localization matrix model representation for the $mathcal N=2$ partition function on $S^4$ we find exact differential relations between the $1/N$ terms in the corresponding free energy $F$ and the $frac{1}{2}$-BPS Wilson loop expectation value $langlemathcal Wrangle$ and also compute their large t Hooft coupling ($lambda gg 1$) expansions. The structure of these expansions is different from the previously studied models without fundamental hypermultiplets. In the more tractable $Sp(2N)$ case we find an exact resummed expression for the leading strong coupling terms at each order in the $1/N$ expansion. We also determine the exponentially suppressed at large $lambda$ contributions to the non-planar corrections to $F$ and $langlemathcal Wrangle$ and comment on their resurgence properties. We discuss dual string theory interpretation of these strong coupling expansions.