The ϵ -Expansions and Boundary/Defect CFTs

The $\epsilon$-expansion is a widely used technique to study aspects of renormalization group flows and critical phenomena. In this talk, I will discuss  recent developments of the $\epsilon$-expansion in the study of boundary and defect universality classes of the O(N) model in d dimensions, with particular focus on the so-called ordinary and normal transitions. I will also discuss  comparisons with numerical approaches, such as conformal bootstrap, Monte Carlo simulations and fuzzy sphere regularizations.