We study half-BPS line defects in $\mathcal{N}=2$ superconformal theories using the bootstrap approach. We concentrate on local excitations constrained to the defect, which means the system is a $1d$ defect CFT with $\mathfrak{osp}(4^*|2)$ symmetry. In order to study correlation functions, we construct a suitable superspace and then use the Casimir approach to calculate a collection of new superconformal blocks. Special emphasis is given to the displacement operator, which controls deformations orthogonal to the defect and is always present in a defect CFT. After writing crossing symmetry we proceed with a numerical and analytical bootstrap analysis. We obtain numerical bounds on the CFT data and compare them to known solutions. We also present an analytic perturbative solution to the crossing equations, and argue that this solution most likely captures line defects in $\mathcal{N}=2$ gauge theories at strong coupling.

中文翻译：

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在 N$$ \mathcal{N} $$ = 2 理论中引导线缺陷

我们使用自举方法研究 $\mathcal{N}=2$ 超共形理论中的半 BPS 线缺陷。我们专注于约束到缺陷的局部激发，这意味着系统是具有 $\mathfrak{osp}(4^*|2)$ 对称性的 $1d$ 缺陷 CFT。为了研究相关函数，我们构造了一个合适的超空间，然后使用 Casimir 方法来计算新的超共形块的集合。特别强调位移算子，它控制与缺陷正交的变形，并且始终存在于缺陷 CFT 中。在写出交叉对称之后，我们继续进行数值和分析引导分析。我们获得 CFT 数据的数值界限，并将它们与已知解决方案进行比较。我们还提出了交叉方程的解析微扰解，