Renormalization group (RG) evolution is a fundamental feature of quantum field theory, playing a pivotal role in both its formal structures and phenomenological applications in particle physics and beyond. While the framework for calculating RG flows is well established, unexpected patterns continue to emerge. In this talk, I will leverage fundamental principles—unitarity and analyticity—to constrain a large sector of RG evolution in effective field theory. This result, analogous to the a-theorem in conformal field theory, can be understood as an infrared avatar of positivity bounds. For phenomenological applications, I will discuss examples in chiral perturbation theory and the Standard Model Effective Field Theory.
