论文标题
在广告中流动的本地顶点操作员$ _3 $
On spectrally flowed local vertex operators in AdS$_3$
论文作者
论文摘要
我们为SL（2，$ \ Mathbb {r} $）中的频谱流动算子提供了一个新颖的本地定义 - WZW模型，在[Arxiv：hepth/0111180]中概括了Maldacena和Ooguri的提案，以供单独使用$ω> 1 $ $ω> 1 $。这使我们能够使用所谓的光谱流操作员在相关器的计算之间建立精确的连接，以及基于本地病房身份的[Arxiv：2105.12130]最近引入的Dei和Eberhardt最近引入的方法。我们表明，后一篇论文中使用的辅助变量$ y $自然来自时空坐标中的分类过程。光谱流相关器满足的递归关系，这些相关器以$ y $ - 空间的形式采用偏微分方程的形式，然后对应于通用光谱流动器的无效条件。我们强调了SL（2，$ \ Mathbb {r} $）串联在此上下文中的作用，并证明了[Arxiv：2105.12130]在$ y $ $ y $ - 空间结构常数的三点函数的有效性，并以任意频谱流动指控。
We provide a novel local definition for spectrally flowed vertex operators in the SL(2,$\mathbb{R}$)-WZW model, generalising the proposal of Maldacena and Ooguri in [arXiv:hep-th/0111180] for the singly-flowed case to all $ω> 1$. This allows us to establish the precise connection between the computation of correlators using the so-called spectral flow operator, and the methods introduced recently by Dei and Eberhardt in [arXiv:2105.12130] based on local Ward identities. We show that the auxiliary variable $y$ used in the latter paper arises naturally from a point-splitting procedure in the space-time coordinate. The recursion relations satisfied by spectrally flowed correlators, which take the form of partial differential equations in $y$-space, then correspond to null-state conditions for generalised spectral flowed operators. We highlight the role of the SL(2,$\mathbb{R}$) series identifications in this context, and prove the validity of the conjecture put forward in [arXiv:2105.12130] for $y$-space structure constants of three-point functions with arbitrary spectral flow charges.
