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Explore the generalized Landau paradigm and symmetry topological field theory in this advanced physics lecture delivered by Apoorv Tiwari at the International Centre for Theoretical Sciences. Delve into the profound transformation occurring in the study of symmetries in quantum many-body systems, examining how new forms of symmetry—including higher-form, non-invertible, and subsystem symmetries—extend far beyond traditional notions in particle and condensed matter physics. Discover how these generalized symmetries provide powerful new frameworks for understanding and classifying quantum phases of matter, including exotic states that fall outside conventional paradigms. Learn about the evolving role of anomalies in condensed matter settings and their central importance in understanding how microscopic symmetries can be realized in highly nontrivial ways at low energies, often protecting or constraining exotic quantum phases such as symmetry-protected topological states. Gain insights into how these developments are reshaping our understanding of quantum entanglement, conservation laws, and hydrodynamics in interacting systems, while beginning to influence approaches to mixed states and open quantum systems. This lecture forms part of a comprehensive program on generalized symmetries and anomalies in quantum phases of matter, designed to provide both conceptual clarity and technical grounding for researchers working at the forefront of these cutting-edge developments in theoretical physics.
