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Explore the fundamental connections between discrete lattice models and continuous field theories through this 58-minute conference talk examining dualities and critical phenomena. Delve into the mathematical frameworks that bridge quantum lattice systems with their continuum counterparts, focusing on how duality transformations reveal hidden symmetries and critical behavior. Learn about the theoretical tools used to map discrete spin systems onto continuous field theories, understanding how phase transitions and scaling properties emerge at the interface between these two descriptions. Discover the role of topological concepts and quantum information theory in characterizing these dualities, with particular emphasis on how critical points serve as natural bridges between lattice and continuum physics. Gain insights into modern approaches for understanding strongly correlated quantum systems through the lens of duality mappings and their applications in condensed matter physics and quantum field theory.
