论文标题
从对称产品CFT到$ {\ rm AD} _3 $
From Symmetric Product CFTs to ${\rm AdS}_3$
论文作者
论文摘要
对称Orbifold CFT中的相关因子由2D时空的可允许的分支盖有限总和给出。我们认为所有操作员都具有较大的扭曲，并表明可以通过penner样矩阵模型来描述相应的分支盖。限制的分支盖是根据该基质模型的光谱曲线给出的，该矩阵模型与覆盖空间上的Strebel二次差异直接相关。因此，时空CFT相关器将覆盖空间解释为双弦理论的世界表，其形式是整个世界单声道模量空间的组成部分，并以nambu-goto般的作用加权。非常引人注目的是，在领先的命令下，此操作也可以写成覆盖地图的Schwarzian的绝对价值。 鉴于对称产品CFT与$ {\ rm Ads} _3 $上的无张力弦理论的等效性，这提供了对arXiv中最初提出的规范弦线双重性的潜在机制的明确实现：Hepth/0504229及其在Arxiv中进一步完善：0803.26813.2681。
Correlators in symmetric orbifold CFTs are given by a finite sum of admissible branched covers of the 2d spacetime. We consider a Gross-Mende like limit where all operators have large twist, and show that the corresponding branched covers can be described via a Penner-like matrix model. The limiting branched covers are given in terms of the spectral curve for this matrix model, which remarkably turns out to be directly related to the Strebel quadratic differential on the covering space. Interpreting the covering space as the world-sheet of the dual string theory, the spacetime CFT correlator thus has the form of an integral over the entire world-sheet moduli space weighted with a Nambu-Goto-like action. Quite strikingly, at leading order this action can also be written as the absolute value of the Schwarzian of the covering map. Given the equivalence of the symmetric product CFT to tensionless string theory on ${\rm AdS}_3$, this provides an explicit realisation of the underlying mechanism of gauge-string duality originally proposed in arXiv:hep-th/0504229 and further refined in arXiv:0803.2681.
