Exactly Solvable 2D Conformal Field Theory - Lecture 2

Delve into the second lecture of a six-part course on exactly solvable two-dimensional conformal field theories (2D CFT). Explore fusion rules and fusion products, correlation functions, Ward identities, crossing symmetry, and conformal blocks. Learn about the bootstrap approach to 2D CFT and gain insights into known exactly solvable CFTs without extended chiral symmetry, including Liouville theory, generalized minimal models, and loop models such as O(n), Potts, and U(n) models. Understand how local conformal symmetry and degenerate fields constrain the spectrum and correlation functions. Examine the crossing symmetry equations and their analytical or numerical solutions, leading to analytic formulas for structure constants. Discover the combinatorial description of correlation functions in loop models, inspired by lattice constructions of statistical models. Gain an overview of current challenges and future directions in solving these models. This comprehensive 2-hour and 9-minute lecture, delivered by Sylvain Ribault from IPhT, is part of the IPhT-TV series and provides a deep dive into the mathematical foundations and applications of exactly solvable 2D CFTs.