标题： $AdS/CFT$中重算符的动力学 显示英文标题

标题： Dynamics of Heavy Operators in $AdS/CFT$

摘要： 在AdS/CFT中的关联函数是通过体几何的完整结构，边界（在CFT中）的算符插入之间的关联。 这些由威滕图表示，在树级上没有量子修正。 一般来说，关联函数具有低标度（或共形）维度，$\Delta$，这与标量算符插入的质量有关，即$\Delta(\Delta - 1) = m^2 L_{AdS}^2$。 在低标度维度下，CFT边界上的算符插入不会对几何度规产生反作用。 另一方面，在与中心荷成比例的大的标度维度下，算符被认为是重的。 这导致了一个有趣的问题，即这种重算符的对偶体几何（AdS）中是什么。 在重极限$\Delta = m L_{AdS}$下，这意味着算符插入的质量也很大。 重算符的两点函数被假定为$(d+1)$维的黑洞，并通过计算作用量来恢复CFT的两点形式。 在$3$维中，由于存在一个称为巴诺多斯度规的精确度规，以及沿边界应力张量插入和将其映射到欧几里得庞加莱上半平面的映射，我们对几何有更多控制。 这些方法用于寻找三点函数的几何结构。 该几何不是简单的黑洞，而是虫洞解，其作用量被计算出来，从而恢复了经典DOZZ公式的“平方”。 在本论文中，我们回顾了arXiv:2306.15105和arXiv:2307.13188的最新工作，以理解AdS/CFT背景下重算符的相关内容。 显示英文摘要

摘要： The correlation function in Ads/CFT are correlation of the operator insertions on the boundary (at CFT) through the complete geometry of bulk. These are represented by Witten diagrams which at tree level doesn't have any quantum corrections. Generally, correlation functions are of low scaling (or conformal) dimension, $\Delta$, which is related to the mass of insertion of the scalar operator by, $\Delta(\Delta - 1) = m^2 L_{AdS}^2$. At low scaling dimensions the operator insertion on the CFT boundary does not back-react the metric of the geometry. On the other hand, at large scaling dimensions which scale with central charge the operator is considered heavy. This leads to an interesting question of what in the dual bulk (AdS) geometry of such heavy operators. At the heavy limit $\Delta = m L_{AdS}$, which means that the mass of the operator insertion is large too. The two-point function of heavy-operator is assumed to be Black hole in $(d+1)$-dimensions and the two-point form of CFT is recovered by calculating the action. In $3$-dimension we have more control over the geometry because of existence of exact metric called Ba\~nados metric with boundary stress-tensor insertion along with a map which maps it to Euclidean Poincare upper half plane. These methods are used to find the geometry for three-point function. The geometry is not simply of a black-hole but a wormhole solution for whose action is calculated which recovers the "square" of the classical DOZZ formula. We review the recent work of arXiv:2306.15105 and arXiv:2307.13188 in this thesis to form an understanding of heavy operators in the context of AdS/CFT.