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Explore advanced concepts in conformal field theory through this comprehensive lecture delivered at the Galileo Galilei Institute, where Dalimil Mazáč continues his systematic treatment of CFT fundamentals and applications. Delve into sophisticated mathematical frameworks and theoretical constructs that form the backbone of modern theoretical physics, building upon previous lectures in this series to develop deeper understanding of conformal symmetries, operator product expansions, and their physical interpretations. Examine the intricate relationships between conformal transformations and quantum field theory, with particular attention to how these concepts apply to critical phenomena and string theory. Learn about the mathematical tools and techniques essential for working with conformal field theories, including the role of primary operators, descendant states, and correlation functions in characterizing conformal field theories. Gain insights into the connections between CFT and other areas of theoretical physics, including statistical mechanics, condensed matter physics, and high-energy physics applications.
