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Explore the intricate relationship between global symmetries and their anomalies in lattice field theory through this 44-minute conference talk delivered at the Institute for Advanced Study's Workshop on Ultra-Quantum Matter. Delve into the theoretical foundations of how global symmetries behave when discretized on a lattice, examining the mathematical structures that give rise to anomalies and their physical implications. Learn about the challenges and techniques involved in preserving or understanding symmetry breaking when transitioning from continuous to discrete spacetime, with particular focus on how these anomalies manifest in quantum many-body systems. Gain insights into cutting-edge research connecting condensed matter physics, quantum field theory, and lattice gauge theory, as the speaker presents advanced concepts relevant to understanding exotic phases of matter and their topological properties.
