聚类和三点函数
Clustering and the Three-Point Function
摘要：
从最近提出的六边形方法开始，我们开发了计算三个重算子的结构常数的分析方法。这样的结构常数是一个半经典的对象，其尺度由扮演普朗克常量角色的算符的倒数长度设定。我们重新制定的六边形扩展的多个轮廓积分和重铸它作为一个总和所产生的集群的残留物的措施的整合。我们测试的方法上两个例子。首先，我们计算了任意耦合下重场的渐近三点函数，并证明了在半经典极限下的结果与强耦合下的弦论计算和以前的树能级结果都是一致的。其次，在一个非BPS和两个BPS运营商在强耦合的情况下，我们总结了所有的包装相关的非平凡运营商的相反的桥梁，或“底部”的镜像通道。我们也给出了另一种解释的结果，在气体的费米子，并表明，它们可以表示为一个运营商值的超行列式competitive。
英文摘要：
We develop analytical methods for computing the structure constant for three heavy operators, starting from the recently proposed hexagon approach. Such a structure constant is a semiclassical object, with the scale set by the inverse length of the operators playing the role of the Planck constant. We reformulate the hexagon expansion in terms of multiple contour integrals and recast it as a sum over clusters generated by the residues of the measure of integration. We test the method on two examples. First, we compute the asymptotic three-point function of heavy fields at any coupling and show the result in the semiclassical limit matches both the string theory computation at strong coupling and the tree-level results obtained before. Second, in the case of one non-BPS and two BPS operators at strong coupling we sum up all wrapping corrections associated with the opposite bridge to the non-trivial operator, or the "bottom" mirror channel. We also give an alternative interpretation of the results in terms of a gas of fermions and show that they can be expressed compactly as an operator-valued super-determinant.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
