论文标题
较大的曲折和较高的$ n $点功能，具有$ s_n $ orbifold CFT的分数保形后代的函数
Larger Twists and Higher $n$-Point Functions with Fractional Conformal Descendants in $S_N$ Orbifold CFTs at Large $N$
论文作者
论文摘要
我们考虑对称产品（$ s_n $）中的相关功能，该Orbifold Cfts大于$ n $，带有任意种子CFT，扩展了我们较早的工作ARXIV：2211.04633。使用覆盖空间技术，我们使用相关器中的分数virasoro发电机来计算下降关系，从祖先的相关因子编写后代的相关因子。我们首先考虑表格（$ m $ -cycle） - （$ n $ -cycle） - （$ q $ -cycle）的情况三点功能，该功能在封面上及其后代的任意初选。在这些示例中，我们表明，最终的下降关系不取决于覆盖空间数据，也不取决于种子CFT的具体细节。这使得这些下降关系在所有$ s_n $ orbifold CFT中通用。接下来，我们将探索表格（2-cycle） - （$ n $ -cycle） - （$ n $ -cycle） - （2-cycle）的四点功能，该功能在封面上的任意初选及其后代。在这种情况下，地图$ s $中的单个参数参数化基本空间交叉比率$ζ_z$和覆盖空间交叉比率$ζ_T$。我们发现，四个点功能的下降关系仅取决于基本空间数据和参数$ s $，我们认为这是根据基本空间数据和基本空间交叉比率编写下降关系的差异。这些下降关系再次不取决于覆盖空间数据，也不取决于种子CFT的细节，这也使这些普遍存在。
We consider correlation functions in symmetric product ($S_N$) orbifold CFTs at large $N$ with arbitrary seed CFT, expanding on our earlier work arXiv:2211.04633 . Using covering space techniques, we calculate descent relations using fractional Virasoro generators in correlators, writing correlators of descendants in terms of correlators of ancestors. We first consider the case three-point functions of the form ($m$-cycle)-($n$-cycle)-($q$-cycle) which lift to arbitrary primaries on the cover, and descendants thereof. In these examples we show that the final descent relations do not depend on the covering space data, nor on the specific details of the seed CFT. This makes these descent relations universal in all $S_N$ orbifold CFTs. Next, we explore four-point functions of the form (2-cycle)-($n$-cycle)-($n$-cycle)-(2-cycle) which lift to arbitrary primaries on the cover, and descendants thereof. In such cases a single parameter in the map $s$ parameterizes both the base space cross ratio $ζ_z$ and the covering space cross ratio $ζ_t$. We find that the descent relations for the four point functions depend only on base space data and the parameter $s$, which we argue is tantamount to writing the descent relations in terms of the base space data and the base space cross ratio. These descent relations again do not depend on the covering space data, nor the specifics of the seed CFT, making these universal as well.
