Introducing defects for O(N) critical models has recently sparked much interest. From a theoretical point of view defects give rise to new universality classes of 3D CFTs that can often be studied analytically. Defects can also describe physical impurities or finite-size effects that can be realised experimentally.
In this talk, I will first review some concepts of renormalisation as well as the epsilon expansion for quantum field theories with quartic interactions. I will then introduce interfaces (defects of co-dimension one) with localised cubic interactions. Going beyond O(N) models, I will show that such defects lead to a large landscape of interface CFTs breaking the symmetry of the original theory to various subgroups.
