Exactly Solvable 2D Conformal Field Theory - Lecture 4: Degenerate 4-Point Functions

Explore the fourth lecture in a six-part series on exactly solvable two-dimensional conformal field theories (2D CFTs). Delve into degenerate 4-point functions and discover analytic formulas for 2-point and 3-point structure constants. Learn how local conformal symmetry and the existence of degenerate fields constrain the spectrum and correlation functions in CFTs. Examine the crossing symmetry equations and their analytical and numerical solutions, leading to precise structure constant formulas. Investigate the bootstrap approach to 2D CFT and gain insights into various exactly solvable models, including Liouville theory, generalized minimal models, and loop models such as O(n), Potts, and U(n). Understand the combinatorial description of correlation functions in loop models, inspired by lattice constructions of statistical models. Discover the current state of research and remaining challenges in solving these models completely.