标题： 面向$K3$sigma模型中拓扑缺陷的分类 显示英文标题

标题： Towards a classification of topological defects in $K3$ sigma models

摘要： 给定一个$K3$表面，超对称非线性 K3 sigma 模型是在 type IIA 超弦理论在$\mathbb{R}^{1,5} \times K3$上的六维紧致化中的内部超共形场论（SCFT）。 这些模型由于在 K3 表面的椭圆指标中发现了 Mathieu 月光现象而受到关注，并在扩展 Mukai 关于$K3$表面辛自同构分类定理中发挥了关键作用。 我们报告了在表征$K3$模型中的拓扑缺陷方面的最新进展（arXiv:2402.08719 [hep-th]），将对称性的概念推广到任意余维子流形上支持的拓扑算符范畴，这些子流形可能具有非可逆的融合规则。 利用 Mukai 格作为 D-膜电荷格的解释，我们通过研究它们与边界态的融合，得到了保留超共形代数和谱流的拓扑缺陷线范畴的一些一般结果。 虽然某些 K3 模型中可能出现无限多个简单缺陷，甚至连续统，但在模空间的一般点上，该范畴实际上是平凡的，即它由恒等缺陷生成。 此外，如果 K3 模型是某些 D-膜 BPS 配置的吸引子点，则所有拓扑缺陷都具有整数量子维度。 我们还提出一个猜想，即当且仅当 K3 模型是环面模型的（可能广义的）轨道时，会出现拓扑缺陷的连续统。 这些一般结果通过重要例子的分析得到了确认。 我们还指出了与最近对 Conway 月光模块理论中拓扑缺陷的研究之间的联系（arXiv:2412.21141 [hep-th], arXiv:2504.18619 [hep-th]）。 显示英文摘要

摘要： Given a $K3$ surface, a supersymmetric non-linear K3 sigma model is the internal superconformal field theory (SCFT) in a six dimensional compactification of type IIA superstring on $\mathbb{R}^{1,5} \times K3$. These models have attracted attention due to the discovery of Mathieu moonshine phenomena for the elliptic genera of K3 surfaces, and have played a pivotal role in extending Mukai's theorem on classification of symplectic automorphisms of $K3$ surfaces. We report on recent progress (arXiv:2402.08719 [hep-th]) in characterizing topological defects in $K3$ models, generalizing the notion of symmetries to categories of topological operators supported on arbitrary codimension submanifolds with possibly non-invertible fusion rules. Taking advantage of the interpretation of Mukai lattice as the D-brane charge lattice, we present a number of general results for the category of topological defect lines preserving the superconformal algebra and spectral flow, obtained by studying their fusion with boundary states. While for certain K3 models infinitely many simple defects, and even a continuum, can occur, at generic points in the moduli space the category is actually trivial, i.e. it is generated by the identity defect. Furthermore, if a K3 model is at the attractor point for some BPS configuration of D-branes, then all topological defects have integral quantum dimension. We also introduce a conjecture that a continuum of topological defects arises if and only if the K3 model is a (possibly generalized) orbifold of a torus model. These general results are confirmed by the analysis of significant examples. We also point out the connection to recent studies of topological defects in the Conway moonshine module theory (arXiv:2412.21141 [hep-th],arXiv:2504.18619 [hep-th]).