Exactly Solvable 2D Conformal Field Theory - Lecture 3

Delve into the intricacies of two-dimensional Conformal Field Theory (CFT) in this comprehensive lecture, part of a series on exactly solvable 2D CFTs. Explore the bootstrap approach to CFT, focusing on the definition of CFTs, diagonal and non-diagonal fields, and degenerate fields. Examine the characteristics of exactly solvable CFTs and their spectrums, 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 contribute to exact solvability, and how these assumptions constrain the spectrum and correlation functions. Investigate the crossing symmetry equations and their analytical or numerical solutions, leading to analytic formulas for structure constants. Gain insights into 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.