Conformal Field Theory - Lecture I

Explore the fundamental principles of Conformal Field Theory in this comprehensive lecture delivered by Dalimil Mazáč at the Galileo Galilei Institute. Delve into the mathematical foundations and physical applications of conformal symmetry, examining how conformal transformations preserve angles while allowing for scaling and rotations. Learn about the conformal group, its representations, and the role of conformal invariance in quantum field theory. Discover the connection between conformal field theories and critical phenomena in statistical mechanics, including phase transitions and scaling behavior. Investigate the operator product expansion, conformal blocks, and the bootstrap approach to understanding conformal field theories. Examine specific examples of conformal field theories, including free field theories and interacting models, while understanding their classification and properties. Gain insights into the relationship between conformal field theory and string theory, AdS/CFT correspondence, and other areas of theoretical physics. Master the techniques for calculating correlation functions, understanding conformal dimensions, and analyzing the structure of conformal field theories through both analytical and numerical methods.