Conformal block study and bounding OPE in conformal field theories

During the past few years, the re-emergence of conformal bootstrap as a numerical tool to solve conformal field theory allowed more precise estimation of several presumed conformal field theory among which we could cite the 3D Ising model. This work intends to provide insight on conformal blocks which are elementary objects in the conformal bootstrap approach. These are considered in Euclidian space where we study fields of all equal dimension. This study allows us to improve bounds derived in \cite{OPEconv}.