A toolbox for defect CFTs

Thanks to the conformal bootstrap, in the last decade there has been a huge progress in understanding CFTs in d dimensions.
 
The bootstrap program has benefited from a set of tools, developed to efficiently deal with the kinematics of CFTs: among them, the embedding space formalism, the radial coordinates, some techniques to compute conformal blocks and to deal with operators with spin. The aim of this talk is to generalize this set of tools to the case of defect conformal field theories, with the hope of extending the bootstrap program to this case.