  We consider strong 't Hooft coupling expansion in special four-dimensional
$\mathcal N=2$ superconformal models that are planar-equivalent to $\mathcal
N=4$ super Yang-Mills theory. Various observables in these models that admit
localization matrix model representation can be expressed at large $N$ in terms
of a Fredholm determinant of a Bessel operator. The latter previously appeared
in the study of level spacing distributions in matrix models and, more
recently, in four-point correlation functions of infinitely heavy half-BPS
operators in planar $\mathcal N=4$ SYM. We use this relation and a suitably
generalized Szego-Akhiezer-Kac formula to derive the strong 't Hooft coupling
expansion of the leading corrections to free energy, half-BPS circular Wilson
loop, and certain correlators of chiral primaries operators in the $\mathcal
N=2$ models. This substantially generalizes partial results in the literature
and represents a challenge for dual string theory calculations in AdS/CFT
context. We also demonstrate that the resulting strong-coupling expansions
suffer from Borel singularities and require adding non-perturbative,
exponentially suppressed corrections. As a byproduct of our analysis, we
determine the non-perturbative correction to the above mentioned four-point
correlator in planar $\mathcal N=4$ SYM.

High Energy Physics - Theory