Current conservation laws associated with continuous symmetries provide concrete information of systems.However, the classically impeccable ``laws\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\'\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\' could be spoiled by quantum mechanical fluctuations, so-called anomalies. The presence of anomalies demands modification of intuition from classical physics. Non-perturbative nature of anomalies advances our understanding in topological phases in condensed matters as well as in high energy physics, for example, matching between ultra-violet and infra-red degrees of freedom.Here, we investigate a different class of anomaly realizations in condensed matters, anomalies in quantum phase transitions between competing orders, described by non-linear sigma models with the Wess-Zumino-Witten term. We explicitly show the universality class of the models is beyond Landau-Ginzburg-Wilson paradigm in even spacetime dimensions, which has been suspected for a while in spite of no concrete results. We discuss candidate symmetric ground states of the models in connection with competing order physics, for example in spin-orbit coupled strongly correlated systems.
