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Explore the field theory foundations of fractons in this comprehensive lecture delivered at the International Centre for Theoretical Sciences as part of the "Generalised symmetries and anomalies in quantum phases of matter" program. Delve into the theoretical framework underlying fracton phases of matter, which represent exotic quantum states characterized by restricted mobility of excitations and emergent subsystem symmetries. Learn how field theoretical approaches provide powerful tools for understanding these unconventional quantum phases that challenge traditional paradigms in condensed matter physics. Examine the mathematical formalism used to describe fracton systems, including their unique conservation laws and the role of higher-form symmetries in constraining particle dynamics. Discover how fracton field theories connect to broader themes in modern quantum many-body physics, including the classification of quantum phases, entanglement patterns, and the emergence of novel hydrodynamic behaviors. Gain insights into the relationship between fracton physics and other exotic quantum phenomena such as symmetry-protected topological states and systems with Hilbert space fragmentation. This pedagogical presentation forms part of a comprehensive program designed to provide conceptual clarity on cutting-edge developments in generalized symmetries and their applications to quantum matter, making it accessible to early-career researchers while maintaining technical rigor for advanced practitioners in theoretical physics.
