A holographic approach to BCFT (a.k.a ICTP Diploma thesis)

In this work, we investigate the holographic approach to the defect crossing equation. More precisely, we use Witten diagrams to study the crossing equation of Conformal Field Theories in the presence of boundaries. We analyze these diagrams and identify the relevant information for the crossing equation. As an example, we compute the Conformal Block decomposition of the boundary and bulk channels in the defect theory and discuss the importance of the results. To first order, we identify that the single trace conformal blocks contributions and the contact diagram conformal block decomposition carries the essential features of the defect crossing equation.