Exactly Solvable 2D Conformal Field Theory - Correlation Functions in Loop Models - Lecture 6

Explore the final lecture in a six-part course on exactly solvable two-dimensional conformal field theory (CFT). Delve into correlation functions in loop models as Sylvain Ribault from IPhT concludes this comprehensive series. Gain insights into the bootstrap approach to 2D CFT and examine 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 the role of local conformal symmetry and degenerate fields in exact solvability, and how these concepts constrain the spectrum and correlation functions. Investigate crossing symmetry equations and their analytical or numerical solutions, leading to analytic formulas for structure constants. Review 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. This 1 hour and 45-minute lecture provides a comprehensive conclusion to the course, offering valuable insights for researchers and advanced students in theoretical physics and mathematical physics.