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arXiv 2005.08890hep-th
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巨大威尔逊圈和AdS $_2$ / dCFT $_1$

Giant Wilson Loops and AdS$_2$/dCFT$_1$

Simone Giombi, Jiaqi Jiang, Shota Komatsu

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91 pages, 19 figures
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摘要：

$\mathcal{N}=4$超对称Yang-Mills理论中的1/2-BPS Wilson环是共形亏损的一个重要例子。特别地，在基本表象中，对于Wilson环上算子插入的相关函数已经做了大量的工作。在本文中，我们将这样的分析扩展到大秩对称和反对称表示中的威尔逊圈，它们对应于具有$AdS_2 \times S^2$和$AdS_2 \times S^4$世界体积几何的探测D3和D5膜，沿着一维轮廓终止于$AdS_5$边界。我们首先计算的相关函数的保护标量插入超对称本地化，并获得一个表示的多重积分是类似的随机矩阵的特征值积分，但具有重要的区别。使用费米气体形式主义和聚类方法的想法，我们评估他们的大$N$限制完全作为一个功能的特胡夫特耦合。结果由类似于量子谱曲线的$Q$函数的多项式的简单积分给出，积分措施取决于插入的数量。接下来，我们研究了AdS中探测D3和D5膜上涨落的相关函数。我们计算选择的三点和四点的功能从扰动理论的D-膜，并表明，他们同意本地化的结果时，仅限于超对称运动学。我们还解释了D3和D5膜的内部几何的差异如何在局部化计算中表现出来。

英文摘要：

The 1/2-BPS Wilson loop in $\mathcal{N}=4$ supersymmetric Yang-Mills theory is an important and well-studied example of conformal defect. In particular, much work has been done for the correlation functions of operator insertions on the Wilson loop in the fundamental representation. In this paper, we extend such analyses to Wilson loops in the large-rank symmetric and antisymmetric representations, which correspond to probe D3 and D5 branes with $AdS_2 \times S^2$ and $AdS_2 \times S^4$ worldvolume geometries, ending at the $AdS_5$ boundary along a one-dimensional contour. We first compute the correlation functions of protected scalar insertions from supersymmetric localization, and obtain a representation in terms of multiple integrals that are similar to the eigenvalue integrals of the random matrix, but with important differences. Using ideas from the Fermi Gas formalism and the Clustering method, we evaluate their large $N$ limit exactly as a function of the 't Hooft coupling. The results are given by simple integrals of polynomials that resemble the $Q$-functions of the Quantum Spectral Curve, with integration measures depending on the number of insertions. Next, we study the correlation functions of fluctuations on the probe D3 and D5 branes in AdS. We compute a selection of three- and four-point functions from perturbation theory on the D-branes, and show that they agree with the results of localization when restricted to supersymmetric kinematics. We also explain how the difference of the internal geometries of the D3 and D5 branes manifests itself in the localization computation.

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