Compactified Imaginary Liouville Theory: Scaling Limits and Challenges

This lecture discusses the compactified imaginary Liouville theory, focusing on the motivations behind studying the scaling limit of loop models. The instructor presents various mathematical challenges associated with this theory, including the framework for non-unitary conformal field theories (CFT). The scaling limits of loop models are explored, referencing key contributions from researchers such as Kondev, Jacobsen, and Saleur. The lecture highlights the significance of critical loops and their connections to mathematical physics, particularly in the context of conformal loop ensembles (CLE). The instructor also addresses higher renormalization schemes and minimal models via BRST, emphasizing the path integral approach. Throughout the lecture, open questions and future directions in the field are presented, providing a comprehensive overview of the current state of research in compactified imaginary Liouville theory and its applications in mathematical physics.