论文标题
$ \ Mathcal {n} = 4 $ sym的集成相关器的大型$ n $扩展
Large $N$ expansion of an integrated correlator in $\mathcal{N}=4$ SYM
论文作者
论文摘要
最近，Dorigoni，Green和Wen猜想了$ \ Mathcal {n} = 4 $ supersymmpersymmetricricric yang-mills理论中的四个超符号主要运算符的集成相关器的显着精确公式。在这项工作中，我们详细研究了它的较大$ n $限制。我们表明，Dorigoni，Green和Wen的公式可以在$（P，Q）$弦的贡献的总和中重新铸造。由于$ sl（2，\ mathbb {z}）$双重性，所有贡献均由单个功能支配，通常以基本字符串贡献出现。该功能的扰动属扩展的大阶行为使我们能够揭示大型$ n $非扰动校正，我们将其解释为全息二型IIB类弦乐理论中的D3-Brane Instantons。通过使用Laplace-Difference方程进行集成相关器，可以更系统地获得相同的结果。
Recently Dorigoni, Green and Wen conjectured a remarkable exact formula for an integrated correlator of four superconformal primary operators in $\mathcal{N}=4$ 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. Due to the $SL(2,\mathbb{Z})$ 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, which we interpret as the D3-brane instantons in the holographically dual type IIB string theory. The same result is obtained more systematically by using a Laplace-difference equation for the integrated correlator.
