Large N expansion of an integrated correlator in $$ \mathcal{N} $$ = 4 SYM

Recently Dorigoni, Green and Wen conjectured a remarkable exact formula for an integrated correlator of four superconformal primary operators in $$ \mathcal{N} $$ N = 4 supersymmetric Yang-Mills theory. In this work, we investigate its large N limit in detail. We show that the formula of Dorigoni, Green and Wen can be recast into the sum over the contributions of ( p, q )-strings via the holography in the large N limit. Due to the SL(2 , ℤ) duality, all the contributions are governed by a single function, typically appearing as the fundamental string contribution. The large order behavior for the perturbative genus expansion of this function allows us to reveal the large N non-perturbative corrections. The same result is obtained more systematically by using a Laplace-difference equation for the integrated correlator.