Institute for Advanced Study, Kyushu University（九州大学高等研究院）；Department of Physics, Kyushu University（九州大学物理系）；Quantum and Spacetime Research Institute (QuaSR), Kyushu University（九州大学量子与时空研究所）
Justin Kaidi
备注：
105 pages; v2: references added; v3: minor corrections
These notes were prepared for a series of intensive lectures delivered at Hokkaido University, Nagoya University, Kyoto University, and Kyushu University.
We begin with a brief review of higher-form symmetries, anomalies, and discrete gauge theories, before introducing non-invertible symmetries in $(1+1)$-dimensional systems. The basic structure of fusion categories is then discussed, including a discussion of categorical analogs of discrete gauging and representation theory. We subsequently turn to $(3+1)$-dimensional theories, where several physical applications of non-invertible symmetries are discussed. These notes are intended to be largely self-contained, and require no prior familiarity with subjects such as conformal field theory or lattice models.
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）
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）
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。
Where Non-Invertible Symmetries End: Twist Defects for Electromagnetic Duality
Center for Theoretical Physics - a Leinweber Institute, Massachusetts Institute of Technology（麻省理工学院理论物理中心-莱因韦伯研究所）；Simons Center for Geometry and Physics, Stony Brook University（石溪大学西蒙斯几何与物理中心）；C. N. Yang Institute for Theoretical Physics, Stony Brook University（石溪大学杨振宁理论物理研究所）
Non-invertible symmetries and mixed anomalies from equations of motion in (3+1)D twisted $BF$ topological quantum field theories
Max Planck Institute for the Physics of Complex Systems（马克斯·普朗克复杂系统物理研究所）；School of Physics, Sun Yat-sen University（中山大学物理学院）；Yau Mathematical Sciences Center, Tsinghua University（清华大学丘成桐数学科学中心）
Additivity, Haag duality, and non-invertible symmetries
Center for Theoretical Physics - a Leinweber Institute, Massachusetts Institute of Technology（麻省理工学院莱因韦伯理论物理中心）；Yang Institute for Theoretical Physics, Stony Brook University（石溪大学杨理论物理研究所）
Non-invertible Symmetries in Weyl Fermions, and Applications to Fermion-Boundary Scattering Problem
Department of Physics, Nanjing University（南京大学物理系）；School of Quantum and Kavli Institute for Theoretical Sciences, University of Chinese Academy of Sciences（中国科学院大学量子学院和理论科学研究所）
