S-duality and correlation functions at large R-charge

We study the ratio of pairs of adjacent correlators of Coulomb-branch operators in SU(2) 𝒩 = 2 sqcd with four flavors within the framework of the large quantum number expansion. Capitalizing on the order-by-order S-duality invariance of the large-R-charge expansion, we compute ab initio the dependence of the leading large- behavior on the marginal coupling τ and we find excellent agreement with numerical estimates from localization.