Title: Line defects in CFTs: Renormalization group flows and semiclassical limits

Abstract: I will discuss line defects in d-dimensional Conformal Field Theories (CFTs). In the first part of the talk, I will argue that the ambient CFT places nontrivial constraints on Renormalization Group (RG) flows on such line defects. I will show that the flow on line defects is consequently irreversible and furthermore a canonical decreasing entropy function exists. This construction generalizes the g theorem to line defects in arbitrary dimensions.  In the second part of the talk, I will present some applications. In particular, I will discuss impurities with large isospin S for some O(3) symmetric theories in the epsilon expansion.  For sufficiently large S diagrammatic perturbation theory breaks down, and these are studied in a semiclassical expansion at fixed epsilon S.