A limit for large R-charge correlators in N $$ \mathcal{N} $$ = 2 theories

Abstract

Abstract Using supersymmetric localization, we study the sector of chiral primary operators (Tr ϕ 2) n with large R-charge 4n in N $$ \mathcal{N} $$ = 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 2n of these operators behave in a simple way, with an asymptotic behavior of the form G2n≈F∞λλ2πe2n $$ {G}_{2n}\approx {F}_{\infty}\left(\uplambda \right){\left(\frac{\uplambda}{2\pi e}\right)}^{2n} $$ n α , modulo O(1/n) corrections, with α=12dimg $$ \alpha =\frac{1}{2} \dim \left(\mathfrak{g}\right) $$ for a gauge algebra g $$ \mathfrak{g} $$ 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=2suN $$ \mathcal{N}=2\kern0.5em \mathfrak{s}\mathfrak{u}(N) $$ gauge theory with 2N fundamental hypermultiplets.

Keywords

• Supersymmetric Gauge Theory
• Conformal Field Theory