Large N Vector Models: Boundary Interactions

This lecture explores 3D large N vector models at the boundary, focusing on boundary RG flows for a 4D scalar field and interactions with degrees of freedom localized on the boundary. Motivations include exploring quantum field theory without locality, coupling to higher-dimensional theories, and searching for examples in perturbation theory. Techniques such as large-N expansion and weak/strong duality are discussed, along with the exploration of possible conformal boundary conditions given a bulk CFT. The lecture also covers the bootstrap for 4D free scalar CFT, condensed matter setups, and the connection between local theories. The study of interacting boundary conditions for free fields and the large-N factorization are highlighted.