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

A bstract As a continuation of the study (in arXiv:2102.07696 and arXiv:2104.12625 ) of strong-coupling expansion of non-planar corrections in N N = 2 4d superconformal models we consider two special theories with gauge groups SU( N ) and Sp(2 N ). They contain N -independent numbers of hypermultiplets in rank 2 antisymmetric and fundamental representations and are planar-equivalent to the corresponding N N = 4 SYM theories. These 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 AdS 5 × S 5 superstring. Starting with the localization matrix model representation for the N 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 1/2 1 2 -BPS Wilson loop expectation value W 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(2 N ) 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 W W and comment on their resurgence properties. We discuss dual string theory interpretation of these strong coupling expansions.