Large N expansion of an integrated correlator in N=4 SYM

Recently Dorigoni, Green and Wen conjectured a remarkable exact formula for an integrated correlator of four superconformal primary operators in 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.

Automated summary

In this work, the large N limit of the integrated correlator of four superconformal primary operators in N = 4 supersymmetric Yang-Mills theory is investigated. The formula proposed by Dorigoni, Green and Wen is shown to be equivalent to the sum over the contributions of (p, q)-strings via holography. The large order behavior of a single function allows for the determination of the large N non-perturbative corrections.