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

A bstract Using supersymmetric localization, we study the sector of chiral primary operators (Tr ϕ 2 ) n with large R -charge 4 n in N N = 2 four-dimensional superconformal theories in the weak coupling regime g → 0, where λ ≡ g 2 n is kept fixed as n → ∞, g representing the gauge theory coupling(s). In this limit, correlation functions G 2 n of these operators behave in a simple way, with an asymptotic behavior of the form G₂ₙ≈ F∞( )(/2π e)²ⁿ G 2 n ≈ F ∞ λ λ 2 π e 2 n n α , modulo O (1 /n ) corrections, with α =1/2 (g) α = 1 2 dim g for a gauge algebra g 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=20.5em su(N) N = 2 s u N gauge theory with 2 N fundamental hypermultiplets.