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Explore the intricate connections between quantum entanglement, symmetry breaking phenomena, and the emerging framework of categorical symmetries in this comprehensive physics lecture delivered at the International Conference on Black holes, Strings and Holography 2025. Delve into advanced theoretical concepts that bridge quantum field theory and condensed matter physics, examining how entanglement measures relate to symmetry-breaking phase transitions and how categorical symmetries provide a more general mathematical framework for understanding these phenomena. Investigate the role of topological defects, anomalies, and higher-form symmetries in quantum many-body systems, while discovering how these concepts apply to both condensed matter systems and high-energy physics contexts including holographic dualities and string theory applications.
