A Scaling Limit for Line and Surface Defects

We study symmetry-breaking line defects in the Wilson-Fisher theory with $O(2N+1)$ global symmetry near four dimensions and symmetry-preserving surface defects in a cubic model with $O(2N)$ global symmetry near six dimensions. We introduce a scaling limit inspired by the large charge expansion in Conformal Field Theory. Using this, we compute the beta function for the defect coupling which allows to identify the corresponding Defect Conformal Field Theories. We also compute the correlation function of two parallel defects as well as correlation functions of certain defect operators with large charge under the surviving symmetry.