对应于基本场的局域变换且保持作用量不变的对称性，会产生（可逆的）拓扑缺陷，这些缺陷遵循类群融合规则。通过指定缺陷一侧的规范不变算子与另一侧此类算子之间的映射，可以构造更一般的（余维为一的）拓扑缺陷。在本工作中，我们将此构造应用于四维麦克斯韦理论和二维自由紧致标量理论。对于麦克斯韦理论，我们证明混合场强$F$及其霍奇对偶$\star F$的拓扑缺陷至多只能是$SO(2)$旋转。对于体耦合和$\theta$角的合理值，我们找到了一个显式的缺陷拉格朗日量，它实现了$SO(2)$角$\phi$的值，使得$\cos\phi$也是有理数。我们进一步确定了此类缺陷对威尔逊线和特胡夫特线的作用，并表明它们通常是非可逆的。我们对二维自由紧致标量$\phi$重复了分析。在这种情况下，我们仅找到四个离散映射：平凡映射、$Z_2$映射$d\phi\rightarrow -d\phi$、类似$\mathcal{T}$对偶的映射$d\phi\rightarrow i \star d\phi$，以及最后两者的乘积。
英文摘要：
Symmetries corresponding to local transformations of the fundamental fields that leave the action invariant give rise to (invertible) topological defects, which obey group-like fusion rules. One can construct more general (codimension-one) topological defects by specifying a map between gauge-invariant operators from one side of the defect and such operators on the other side. In this work, we apply such construction to Maxwell theory in four dimensions and to the free compact scalar theory in two dimensions. In the case of Maxwell theory, we show that a topological defect that mixes the field strength $F$ and its Hodge dual $\star F$ can be at most an $SO(2)$ rotation. For rational values of the bulk coupling and the $θ$-angle we find an explicit defect Lagrangian that realizes values of the $SO(2)$ angle $φ$ such that $\cos φ$ is also rational. We further determine the action of such defects on Wilson and 't Hooft lines and show that they are in general non-invertible. We repeat the analysis for the free compact scalar $ϕ$ in two dimensions. In this case we find only four discrete maps: the trivial one, a $Z_2$ map $dϕ\rightarrow -dϕ$, a $\mathcal{T}$-duality-like map $dϕ\rightarrow i \star dϕ$, and the product of the last two.
Symmetry TFTs and Anomalies of Non-Invertible Symmetries
已知可逆整体对称性的t Hooft反常可以用高维可逆TQFT来刻画。对于不可逆对称，类似的陈述还有待理解。在这篇文章中，我们讨论了如何在一个不可逆的TQFT称为对称TFT（对称TFT）的链接不变量可以被用来作为一个诊断的不可逆对称的特胡夫特异常。当不可逆对称是非本质不可逆的，因此SymTFT是Dijkgraaf-Witten模型时，可以显式计算连接不变量。我们通过2d阿贝尔Higgs模型和4d伴随QCD和$\mathcal{N}=4$ super Yang-Mills模型的例子来说明这个建议。我们还评论如何不可逆对称性的特胡夫特异常施加新的约束的动态。
Spontaneous breaking of non-invertible symmetries and duality to beyond-Landau transitions
Institute for Quantum Information and Matter, California Institute of Technology（加州理工学院量子信息物质研究所）；Department of Physics, California Institute of Technology（加州理工学院物理系）；Institute of Physics, Chinese Academy of Sciences（中国科学院物理研究所）；Department of Physics, Harvard University（哈佛大学物理系）；Department of Physics and Center for Theory of Quantum Matter, University of Colorado, Boulder（科罗拉多大学博尔德分校物理系与量子物质理论中心）；C.N. Yang Institute for Theoretical Physics, Stony Brook University（纽约州立大学石溪分校杨振宁理论物理研究所）
$\mathcal{N}=2$ RG flows, Non-Invertible Symmetries and Matrix Factorisations
Perimeter Institute for Theoretical Physics（Perimeter理论物理研究所）；Institut für Theoretische Physik, ETH Zurich（苏黎世联邦理工学院理论物理研究所）；Yukawa Institute for Theoretical Physics, Kyoto University（京都大学汤川理论物理研究所）
Non-Invertible Symmetries and Boundaries for Two-Dimensional Fermions
INFN, Sezione di Trieste（意大利国家核物理研究所的里雅斯特分部）；Department of Applied Mathematics and Theoretical Physics, University of Cambridge（剑桥大学应用数学与理论物理系）；Abdus Salam Centre for Theoretical Physics, Imperial College London（伦敦帝国理工学院阿卜杜斯·萨拉姆理论物理中心）；SISSA（的里雅斯特国际高等研究学院）
