I will discuss line defects in the O(N) model at the Wilson-Fisher fixed point from the point of view of the analytic conformal bootstrap. These defects represent magnetic impurities in condensed matter systems, such as quantum antiferromagnets. After reviewing a recently derived conformal dispersion relation, I will apply it to compute the two-point functions of bulk operators in the presence of a localized magnetic field or a spin impurity in the critical O(N) model. Finally, I will discuss the defect and bulk CFT data that one can extract from it.

City University London