Conformal Field Theory in dimensions greater than two - Analysis of Conformal Defects with the Embedding Formalism

In the first part of this work we give an overview of the main results for the conformal field theory; we focus on the constraint imposed by the conformal symmetry on the correlation function of primary operators giving explicit examples in the scalar case and we discuss the methods used to pull out the CFT data from the crossing equation. In the second part we employ the embedding formalism in order to simplify the study of conformal field theory; we make use of it to analyze the constraints imposed by the residual symmetry as result of the insertion of a flat or spherical defect. Finally we focus on the study of the two-point functions of local operators in the bulk and defect channel through their OPE decompositions and we comment on the special case of a defect of codimension two.