UC San Diego

Symmetry, anomaly and duality put strong constraints on the low-energy physics of the quantum field theory. In this dissertation, we used generalized symmetry and symmetry anomaly to investigate the quantum phases of matter and their transitions. In particular, we studied the generalized exact duality in 1+1d systems and infrared duality for 2+1d gauge theories. We investigated the 't Hooft anomaly matching of non-linear sigma model with the Wess-Zumino-Witten term. We focus on the implications of these non-perturbative methods on 1+1d quantum phase transitions, 2+1d deconfined quantum criticality and Fermi surface symmetric mass generation.