Exact Three- and Four-Point Correlation Functions in O(n) and Potts Loop Models

Explore a conference talk on exact three- and four-point correlation functions in O(n) and Potts loop models presented by Jesper Jacobsen from École Normale Supérieure. Delve into an overview of recent work on geometrically defined bulk correlators in two-dimensional conformally invariant loop models, corresponding to combinatorial maps that describe connectivities between insertion points. Examine selected three-point correlators, including probabilities of three points belonging to the same loop, two loops coming close together in three points, and an open curve running between two points passing through a third point. Discover how three-point correlators have closed expressions using special functions, while four-point correlators require more advanced techniques. Learn about the combination of global symmetry in Conformal Field Theory (CFT), cellular algebra of lattice discretization, and interchiral conformal bootstrap used to determine four-point correlators. Investigate the structure of the 235 simplest four-point structure constants, composed of a universal function of conformal dimensions and a polynomial function of loop weights. Gain insights into how polynomial factors, isolated through amplitude ratios, are retrieved in lattice models and remain independent of lattice size and critical point status.