The N=4 Defect Bootstrap

We consider a  supersymmetric Wilson line in N=4 SYM decorated with four insertions of local operators. The system is effectively a one-dimensional supersymmetric CFT and we constrain it by using the superconformal bootstrap. We analyze in particular the mixed system of correlation functions involving the displacement operator and its simplest partner. We derive the superconformal Ward identities as well as the crossing equations and obtain strong bounds on the OPE coefficients and conformal dimensions of various operators. Our results can in particular be used to compute the anomalous dimensions of the first long operator at strong coupling without using perturbation theory.