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Explore the fundamental concepts of global symmetry anomalies in lattice quantum systems through this advanced theoretical physics seminar from the Institute for Advanced Study. Delve into the precise mathematical definition of invertible symmetries and anomalies in lattice systems, understanding how anomalies represent intrinsic properties of symmetry actions independent of any specific Hamiltonian. Discover the surprising finding that lattice anomalies do not correspond one-to-one with 't Hooft anomalies in continuum quantum field theories, despite the existence of a mapping between them that is neither injective nor surjective. Learn about the significant implications of lattice anomalies for commuting projector Hamiltonians and many-body localization phenomena. Examine the classification framework for these anomalies and understand how the techniques developed for characterizing lattice system anomalies could provide new insights into quantum field theory anomalies. This presentation bridges condensed matter physics and high-energy theory, offering a rigorous mathematical treatment of topological features in quantum many-body systems while highlighting the distinctions between discrete lattice formulations and continuum field theories.
