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 $$ \mathcal{N} $$ 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 $$ \mathcal{N} $$ N = 4 SYM theories. These $$ \mathcal{N} $$ 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 AdS5 × S5 superstring. Starting with the localization matrix model representation for the $$ \mathcal{N} $$ N = 2 partition function on S4 we find exact differential relations between the 1/N terms in the corresponding free energy F and the $$ \frac{1}{2} $$ 1 2 -BPS Wilson loop expectation value $$ \left\langle \mathcal{W}\right\rangle $$ W and also compute their large ’t Hooft coupling (λ » 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 λ contributions to the non-planar corrections to F and $$ \left\langle \mathcal{W}\right\rangle $$ W and comment on their resurgence properties. We discuss dual string theory interpretation of these strong coupling expansions.