Generalized symmetries in ordered phases and applications to disordering

In this talk, we show that higher-form and non-invertible symmetries generally emerge in ordered phases and discuss their ability to predict and classify phase transitions into neighboring disordered phases. These transitions are driven by spontaneously breaking the emergent generalized symmetries. While the resulting phase is disordered, it is nontrivial, hosting (non-)abelian topological order, emergent gauge bosons, and fractionalized symmetry charges. We will highlight a few simple examples but focus on an isotropic antiferromagnet in 3D space. Using the emergent generalized symmetries (which include higher-form and non-invertible symmetries), we show that there exists a transition out of the antiferromagnetic phase to a paramagnetic phase that has emergent photons and a gapless mode that behaves like an emergent axion. These results demonstrate that even the most exotic generalized symmetries emerge in ordinary phases and provide a valuable framework for characterizing them and their transitions.