Currents in the O(n) Model: Conformal Field Theory Insights

This lecture discusses the O(n) model on the hexagonal lattice, focusing on the behavior of currents within this framework. The instructor introduces the model by explaining the configuration of mutually avoiding loops and the associated partition function, which incorporates weights for monomers and loops. The critical points of the model are highlighted, particularly the transition between dilute and dense phases, and their implications for conformal field theory (CFT). The instructor references foundational work by Cardy, addressing both successes and necessary corrections in understanding the model's properties. The lecture further explores the implications of non-locality in the O(n) model and the significance of the conserved U(1) current. The discussion includes the spectrum of critical exponents and the role of primary operators in the context of global O(n) symmetry. The instructor concludes by presenting recent findings on the chiral anomaly, emphasizing the differences in methodologies used to derive results compared to earlier works, and invites questions from the audience.