论文标题
电流 - 电流变形，共形积分和相关函数
Current-current deformations, conformal integrals and correlation functions
论文作者
论文摘要
最近研究了$ t \ bar {t} $ - 2D CFTS的类型变形的动机，这是ADS $ _3 $/CFT $ _2 $的ADS $ _3 $ _3 $/CFT $ sossonence的特定类别的单条形变形。从世界表的角度来看，这对应于广告$ _3 $上$σ$ - 模型的边际变形，该$ _3 $产生了一个字符串背景，该字符串背景在ADS $ _3 $和平面线性Dilaton解决方案之间进行了插值。在这里，为了进一步研究这个世界表CFT，我们将其考虑在边界的存在下。在上一篇论文中，我们计算了该理论在磁盘上的不同相关函数，包括批量的1分函数，边界 - 边界 - 边界2分函数和散装 - 边界的2分函数。这使我们计算了散装和边界顶点算子的异常尺寸，这首先需要适当地正规化保形积分的紫外线差异。在这里，我们通过计算磁盘上的散装bulk 2点函数来扩展分析，并在球体上的其他可观察力。我们证明，在我们以前的作品中提出的顶点运算符的重归其化与Sphere $ n $ - 点函数的形式一致。
Motivated by the recent work on $T\bar{T}$-type deformations of 2D CFTs, a especial class of single-trace deformations of AdS$_3$/CFT$_2$ correspondence has been investigated. From the worldsheet perspective, this corresponds to a marginal deformation of the $σ$-model on AdS$_3$ that yields a string background that interpolates between AdS$_3$ and a flat linear dilaton solution. Here, with the intention of studying this worldsheet CFT further, we consider it in the presence of a boundary. In a previous paper, we computed different correlation functions of this theory on the disk, including the bulk 1-point function, the boundary-boundary 2-point function, and the bulk-boundary 2-point function. This led us to compute the anomalous dimension of both bulk and boundary vertex operators, which first required a proper regularization of the ultraviolet divergences of the conformal integrals. Here, we extend the analysis by computing the bulk-bulk 2-point function on the disk and other observables on the sphere. We prove that the renormalization of the vertex operators proposed in our previous works is consistent with the form of the sphere $N$-point functions.
