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As a continuation of the study (in arXiv:2102.07696 and arXiv:2104.12625) ofstrong-coupling expansion of non-planar corrections in $\mathcal N=2$ 4dsuperconformal models we consider two special theories with gauge groups$SU(N)$ and $Sp(2N)$. They contain $N$-independent numbers of hypermultipletsin rank 2 antisymmetric and fundamental representations and areplanar-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 afinite number of D7-branes and O7-plane; the dual string theories should beparticular orientifolds of $AdS_5\times S^5$ superstring. Starting with thelocalization matrix model representation for the $\mathcal N=2$ partitionfunction on $S^4$ we find exact differential relations between the $1/N$ termsin the corresponding free energy $F$ and the $\frac{1}{2}$-BPS Wilson loopexpectation value $\langle\mathcal W\rangle$ and also compute their large 'tHooft coupling ($\lambda \gg 1$) expansions. The structure of these expansionsis different from the previously studied models without fundamentalhypermultiplets. In the more tractable $Sp(2N)$ case we find an exact resummedexpression 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 $\langle\mathcalW\rangle$ and comment on their resurgence properties. We discuss dual stringtheory interpretation of these strong coupling expansions.

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