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arXiv 2003.11016hep-th
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$\mathcal{N}=4$超级阳磨机缺陷的抑制

Taming Defects in $\mathcal{N}=4$ Super-Yang-Mills

Yifan Wang

备注：
91 pages, 2 figures; v3: minor corrections and more references added
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摘要：

本文研究了四维${\cal N}=4$超杨-米尔斯（SYM）系统中包含扩展缺陷算子的关联函数.主要的工具是超对称本地化相对于超荷$\cal Q$在\cite{Pestun:2009nn}中引入的计算观测值的$\cal Q$ -上同调。我们对${\cal N}=4$ SYM中属于$\cal Q$ -上同调的不同余维的一般缺陷进行了分类，它们形成了${1\over 16}$ -BPS缺陷网络。通过对四维半球上的${\cal N}=4$ SYM进行$\cal Q$ -局部化，我们发现了二维半球上的子流形上的一个新的缺陷-杨-米尔斯（dYM）理论，该子流形由边界圆上的（约束）二维杨-米尔斯耦合到拓扑量子力学来描述.这也通过折叠技巧推广到${\cal N}=4$ SYM中的界面缺陷。我们提供了明确的字典之间的缺陷可观的SYM和那些在dYM，这使得提取一般${1\over 16}$ -BPS缺陷网络可观的SYM从二维规范理论和矩阵模型技术。应用于$SU(N)$ SYM中的D5膜界面，我们明确地确定了一组在大$N$极限下的缺陷关联函数，并获得了与$AdS_5\times S^5$上IIB超引力强耦合结果的精确匹配。

英文摘要：

We study correlation functions involving extended defect operators in the four-dimensional ${\cal N}=4$ super-Yang-Mills (SYM). The main tool is supersymmetric localization with respect to the supercharge $\cal Q$ introduced in \cite{Pestun:2009nn} which computes observables in the $\cal Q$-cohomology. We classify general defects of different codimensions in the ${\cal N}=4$ SYM that belong to the $\cal Q$-cohomology, which form ${1\over 16}$-BPS defect networks. By performing the $\cal Q$-localization of the ${\cal N}=4$ SYM on the four-dimensional hemisphere, we discover a novel defect-Yang-Mills (dYM) theory on a submanifold given by the two-dimensional hemisphere and described by (constrained) two-dimensional Yang-Mills coupled to topological quantum mechanics on the boundary circle. This also generalizes to interface defects in ${\cal N}=4$ SYM by the folding trick. We provide explicit dictionary between defect observables in the SYM and those in the dYM, which enables extraction of general ${1\over 16}$-BPS defect network observables of the SYM from two-dimensional gauge theory and matrix model techniques. Applied to the D5 brane interface in the $SU(N)$ SYM, we explicitly determine a set of defect correlation functions in the large $N$ limit and obtain precise matching with strong coupling results from IIB supergravity on $AdS_5\times S^5$.

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