Bootstrapping Holographic Defect Correlators

The study of defect CFT generally aims at understanding how the dynamics of a bulk theory are affected by the presence of a defect. When the symmetry is broken, correlation functions of local operators do not obey the rules of conformal symmetry anymore. In this chapter, we study two-point functions of scalar operators in the presence of a line defect, using modern analytic bootstrap methods. We show in particular that two-point functions of scalar operators can be reconstructed from an elegant dispersion relation, and apply this method to the special case where the bulk theory is four-dimensional \({\mathcal {N}}=4\) Super Yang-Mills, with the defect being the supersymmetric Wilson line.