论文标题
关于ADS/CFT通信中的联系项和共形歧管的评论
Comments on contact terms and conformal manifolds in the AdS/CFT correspondence
论文作者
论文摘要
我们研究了使用AD/CFT对应关系确切的边缘运算符相关函数中出现的接触术语。众所周知，具有准确边缘变形的CFT需要存在接触项的存在，其系数在保形歧管的背景下具有几何解释。我们表明，广告/CFT对应关系正确捕获了CFT分析所期望的相关函数的数学结构。为此，我们采用全息RG来制定批量上最通用的设置，以描述精确的边缘变形。所得的运动的大体方程是非线性的，并扰动地求解以获得壳动作。我们使用GKP-witten处方计算精确边缘运算符的三分和四点函数，并证明它们与预期结果匹配。批量中的截止表面处方是边界CFT中共形扰动理论的正规化方案。作为应用程序，我们检查了四点函数的双重OPE极限。双重痕量运算符的异常维度是根据保形歧管的几何数据编写的。
We study the contact terms that appear in the correlation functions of exactly marginal operators using the AdS/CFT correspondence. It is known that CFT with an exactly marginal deformation requires the existence of the contact terms with their coefficients having a geometrical interpretation in the context of conformal manifolds. We show that the AdS/CFT correspondence captures properly the mathematical structure of the correlation functions that is expected from the CFT analysis. For this purpose, we employ holographic RG to formulate a most general setup in the bulk for describing an exactly marginal deformation. The resultant bulk equations of motion are nonlinear and solved perturbatively to obtain the on-shell action. We compute three- and four-point functions of the exactly marginal operators using the GKP-Witten prescription, and show that they match with the expected results precisely. The cut-off surface prescription in the bulk serves as a regularization scheme for conformal perturbation theory in the boundary CFT. As an application, we examine a double OPE limit of the four-point functions. The anomalous dimensions of double trace operators are written in terms of the geometrical data of a conformal manifold.
