An Introduction to Anomalies in Quantum Field Theories

Explore the fundamental concepts of anomalies in quantum field theories through this comprehensive lecture delivered at the International Centre for Theoretical Sciences. Delve into the theoretical foundations of anomalies, which have evolved from their origins in high-energy physics to become crucial tools for understanding quantum many-body systems and condensed matter physics. Learn how anomalies relate to the broader framework of generalized symmetries, including higher-form, non-invertible, and subsystem symmetries that extend beyond traditional particle and condensed matter paradigms. Discover the role of anomalies in protecting and constraining exotic quantum phases, particularly symmetry-protected topological states, and understand their impact on quantum entanglement, conservation laws, and hydrodynamics in interacting systems. Gain insights into how anomalies influence the realization of microscopic symmetries at low energies and their applications to mixed states and open quantum systems. This pedagogical presentation forms part of a comprehensive program on generalized symmetries and anomalies in quantum phases of matter, designed to provide conceptual clarity and technical grounding for researchers working at the intersection of quantum field theory and condensed matter physics.