The planar limit of the $\mathcal{N} = 2$ $\mathbf{E}$-theory: numerical calculations and the large $\lambda$ expansion

We study correlation functions of local operators and Wilson loop expectation values in the planar limit of a 4d $\mathcal{N}=2$ superconformal ${\rm SU}(N)$ YM theory with hypermultiplets in the symmetric and antisymmetric representations of the gauge group. This so-called $\mathbf{E}$ theory is closely related to $\mathcal{N}=4$ SYM and has a holographic description in terms of a $\mathbb{Z}_2$ orientifold of AdS$_5\times S^5$. Using recent matrix model results based on supersymmetric localization we develop efficient numerical methods to calculate two- and three-point functions of certain single trace operators as well as 1/2-BPS Wilson loop expectation values as a function of the 't Hooft coupling $\lambda$. We use our numerical results to arrive at simple analytic expressions for these correlators valid up to the sixth order in the $\lambda^{-1/2}$ strong coupling expansion. These results provide explicit field theory predictions for the $\alpha'$ corrections to the supergravity approximation of type IIB string theory on the AdS$_5\times S^5/\mathbb{Z}_2$ orientifold.