Most of the known non-invertible symmetries of quantum field theories in three and four spacetime dimensions act invertibly on local operators. An exception is coset symmetries, which can be constructed from gauging a non-normal subgroup of an invertible symmetry. In this paper, we study the action of a general finite non-invertible symmetry on local operators in four dimensions. We show that non-invertible symmetries without topological line operators necessarily act invertibly on local operators. Using this result, we argue that the action of a general non-invertible symmetry in 3+1d on local operators can be decomposed into the invertible action of some operators composed with the action of a gauging interface. We use this result to study when such a symmetry is anomaly-free. We find a necessary condition for a finite non-invertible symmetry in 3+1d to be anomaly-free, and show that anomaly-free non-invertible symmetries without topological line operators are non-intrinsically non-invertible.
Generalized Wigner theorem for non-invertible symmetries
Indiana University（印第安纳大学）；Institute for Advanced Study, Princeton（普林斯顿高等研究院）；Rice University（莱斯大学）；Washington University in St. Louis（华盛顿大学圣路易斯分校）；Brookhaven National Laboratory（布鲁克海文国家实验室）；Technische Universität Chemnitz（开姆尼茨工业大学）；Indian Institute of Technology Madras（印度马德拉斯理工学院）
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）
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。
Lattice Models for Phases and Transitions with Non-Invertible Symmetries
Mathematical Institute, University of Oxford（牛津大学数学研究所）；Niels Bohr International Academy, Niels Bohr Institute, University of Copenhagen（哥本哈根大学尼尔斯·玻尔学院，尼尔斯·玻尔研究所）
Unveiling dynamical quantum error correcting codes via non-invertible symmetries
International Centre for Theoretical Physics（国际理论物理中心）；Mathematical Institute, University of Oxford（牛津大学数学研究所）；Simons Center for Geometry and Physics, Stony Brook University（石溪大学西蒙几何与物理中心）；Mani L. Bhaumik Institute for Theoretical Physics, Department of Physics and Astronomy, University of California, Los Angeles（加州大学洛杉矶分校物理学与天文学系马尼·L·巴乌米克理论物理研究所）；C. N. Yang Institute for Theoretical Physics, Stony Brook University（石溪大学杨振宁理论物理研究所）
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 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）
