A limit for large R-charge correlators in N = 2 theories

Using supersymmetric localization, we study the sector of chiral primary operators (Tr ϕ²)ⁿ with large R-charge 4n in N = 2 four-dimensional superconformal theories in the weak coupling regime g → 0, where λ ≡ g²n is kept fixed as n → ∞, g representing the gauge theory coupling(s). In this limit, correlation functions G_2n of these operators behave in a simple way, with an asymptotic behavior of the form G2n≈F(λ2πe)2nn^α, modulo O(1/n) corrections, with α=12dim(g) for a gauge algebra g and a universal function F_∞(λ). As a by-product we find several new formulas both for the partition function as well as for perturbative correlators in N=2su(N) gauge theory with 2N fundamental hypermultiplets.