“An ‘t Hooft anomaly is an obstruction to gauge global symmetries and constrains low-energy behaviors of a system. In this talk, we focus on the 3D CP^N model, an effective field theory of quantum anti-ferromagnets, and derive a mixed ‘t Hooft anomaly between the refection and magnetic symmetries. To detect the ‘t Hooft anomaly, we insert a flux for the reflection symmetry by putting the model on a non-orientable manifold. Then, we find an obstruction to gauge the magnetic symmetry. This anomaly indicates that even when the flavor symmetry is broken explicitly, the model doesn’t admit a unique gapped ground state as long as the refection and magnetic symmetries are respected. As an application, we also discuss the finite-temperature phase diagram of the CP^N model. This talk is based on: T.F., M. Hongo, “Global anomaly matching in the higher-dimensional $¥mathbb{CP}^{N?1}$ model”, PRB. 101, 155113, (2020).”