Defects in the long-range O(N) model

We initiate the study of extended excitations in the long-range O(N) model. We focus on line and surface defects and we discuss the challenges of a naive generalization of the simplest defects in the short-range model. To face these challenges we propose three alternative realizations of defects in the long-range model. The first consists in introducing an additional parameter in the perturbative RG flow or, equivalently, treating the non-locality of the model as a perturbation of the local four-dimensional theory. The second is based on the introduction of non-local defect degrees of freedom coupled to the bulk and it provides some non-trivial defect CFTs also in the case of a free bulk, i.e. for generalized free field theory. The third approach is based on a semiclassical construction of line defects. After finding a non-trivial classical field configuration we consider the fluctuation Lagrangian to obtain quantum corrections for the defect theory.