Renormalization Program: Fixed Points and Couplings

This lecture delves into the concept of fixed points and couplings in the context of the renormalization program. The instructor explains how the behavior of couplings changes with energy scales, leading to the identification of UV and IR fixed points. By analyzing the beta function, the lecture explores scenarios where couplings either approach zero in the UV or IR regimes. The implications of marginally relevant interactions and the hierarchy of scales are discussed, highlighting how complex low-energy phenomena emerge from simple dynamics. The lecture also touches upon conformal perturbation theory and the significance of fixed points in understanding the behavior of operators in a theory.