Liu, Ruizhi2024-10-042024-10-042024-10-01http://hdl.handle.net/10222/84637Symmetry and topology are guiding principles in physics, while anomalies represent the intersection of these concepts. Roughly speaking, a (’t Hooft) anomaly indicates that symmetry is violated in a topological manner in the presence of background gauge fields. The topological nature of anomalies makes them robust under symmetric deformations. As a consequence, it puts constraints on the low energy behavior of interesting physical models. In this thesis, I will briefly review the basic concepts and constructions of gauging and anomalies. Then I will apply these ideas to Kitaev spin-S model, which is potentially a platform for quantum spin liquid. I will also explain some of applications of anomalies to high-energy physics, such as string theory.Symmetry and topology are guiding principles in physics, while anomalies represent the intersection of these concepts. Roughly speaking, a (’t Hooft) anomaly indicates that symmetry is violated in a topological manner in the presence of background gauge fields. The topological nature of anomalies makes them robust under symmetric deformations. As a consequence, it puts constraints on the low energy behavior of interesting physical models. In this thesis, I will briefly review the basic concepts and constructions of gauging and anomalies. Then I will apply these ideas to Kitaev spin-S model, which is potentially a platform for quantum spin liquid. I will also explain some of applications of anomalies to high-energy physics, such as string theory.enSymmetriesQuantum field theoriesAnomaliesThesis