AI 中文总结
本文利用AdS/CFT对应关系，在N=4超杨-米尔斯理论强耦合下计算Wilson圈期望值，分析含单个尖点的Wilson线的鞍点与尖点反常维数，还推广至双尖点Wilson圈及其他规范理论软函数的可能情况。
AI 中文摘要
由以一定角度（尖点）相交的Wilson线构成的算符的重整化涉及所谓的尖点反常维数，这是量子色动力学（QCD）中诸多过程里出现的普适量，源于胶子相互作用的发散。本文中，我们考虑在横向方向分离的一对带尖点的Wilson线的真空期望值，该构型可与重夸克横向动量依赖（TMD）碎裂中的一个简单观测量以及TMD软函数相关联。我们利用AdS/CFT对应关系计算N=4超杨-米尔斯理论中强耦合下Wilson圈的期望值，这一方法与尖点反常维数的微扰计算互为补充。我们首先直接在闵氏符号下对含单个尖点的Wilson线构型的Nambu-Goto作用量及其鞍点展开详尽分析，发现存在两类不同的鞍点，其贡献在参数空间的不同区域占主导。我们从该构型计算Δη在全范围、Δθ=0和Δθ=π情形下的尖点反常维数Γ_cusp[Δη,Δθ]，并与文献中的已有结果对比。随后，我们运用所发展的技术计算具有横向分离的双尖点Wilson圈的期望值，确定大快度极限下极值面上的横向坐标轮廓。我们还讨论了该构型与结果向具有全息对偶的其他规范理论中软函数的可能推广。
英文摘要
The renormalization of operators built out of Wilson lines that meet at an angle (cusp) involve what is known as the cusp anomalous dimension, a universal object appearing in many processes in QCD due to the divergences from gluonic interactions. In this paper, we consider the vacuum expectation value of a pair of cusped Wilson lines separated in the transverse direction. This configuration can be related to a simple observable in heavy quark transverse momentum-dependent (TMD) fragmentation as well as the TMD soft function. We compute the expectation values of Wilson loops in $N=4$ super Yang-Mills theory at strong coupling via the AdS/CFT correspondence, an approach complementary to perturbative calculations of the cusp anomalous dimension. We first present a thorough analysis, directly in Minkowski signature, of the Nambu-Goto action and its saddle points for a Wilson line configuration with a single cusp. We find that there are two different classes of saddle points whose contributions dominate different regions of parameter space. We calculate the cusp anomalous dimension $Γ_{\rm cusp}[Δη, Δθ]$ for the whole range of $Δη$ from this setup, focusing on the cases $Δθ= 0$ and $Δθ= π$, and compare it with previous results in literature. We then use the techniques we developed to compute the expectation value of the two-cusp Wilson loop with transverse separation, and determine the profile of the transverse coordinate on the extremal surface in the large rapidity limit. We discuss the possible generalizations of our setup and results to soft functions in other gauge theories with a holographic dual.
Commentsv2, 64 pages, 18 figures
