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Explore advanced concepts in conformal field theory through this comprehensive lecture delivered at the Galileo Galilei Institute, where theoretical physicist Dalimil Mazáč presents the third installment of his series on this fundamental area of theoretical physics. Delve into the mathematical framework that describes scale-invariant quantum field theories, examining how conformal symmetry constrains physical systems and leads to powerful computational techniques. Learn about the conformal bootstrap program, correlation functions, and operator product expansions while discovering how these tools apply to critical phenomena in statistical mechanics and string theory. Gain insights into modern developments in the field, including numerical bootstrap methods and their applications to solving strongly coupled quantum field theories. This 93-minute academic lecture builds upon previous material in the series and provides rigorous mathematical treatment suitable for graduate students and researchers in theoretical physics.
