AdS/CFT 对偶给出全息原理一种非常漂亮的具体表述，它比其它引力/规范场对偶的表述更加清晰和准确，同时它为强相互作用的研究提供了一种重要的方法。我们可以通过研究非局域算子加深对AdS/CFT对偶的理解。在本项目中，我们首先计算基础表示和反对称表示的Wilson surfaces算子的关联函数。这时关联函数有两种可能的首阶项的贡献，第一种是M2膜以Wilson surface 算子为边界，M2膜与M5膜之间交换无质量的粒子，另一种主要贡献是M2膜以M5膜和Wilson surface算子为边界。我们希望找到在Wilson surface的情况下也有Gross-Ooguri相变。Wilson surfaces算子完成后，我们还将讨论Wilson loops算子与局域算子的关联函数。

The AdS/CFT duality beautifully exemplified the idea of holography in clarity and precision, more powerfully than any other examples of the gravity/field theory correspondence, it also provides a powerful method to study strongly coupled gauge theory. We can gain deeper understanding of AdS/CFT duality by studying nonlocal operators in the context of AdS/CFT Correspondence. This project is first to compute the correlation function of fundamental and anti-symmetric Wilson surfaces. There are two possible leading contributions to the correlation. One is a M2-brane bounded by Wilson surface with massless propagating modes connecting the M2-brane and the M5-brane. The other is an M2-brane whose boundaries are attached to the M5-brane and Wilson surface. We will find that the Gross-Ooguri phase transition also exist in Wilson surface case. Then, we will study correlation functions of Wilson loops and local operators.