Anomalies

Several interesting applications of Abelian and non-Abelian discrete symmetries have been studied in particle physics such as flavor physics (see Chap. 19 ). In general, symmetries at the tree-level can be broken by quantum effects, that is, anomalies. When symmetries are anomalous, symmetry breaking terms are induced. On the other hand, symmetries should be anomaly-free to be exact even including any quantum effects.