Speaker: Jean-François Fortin
Conformal field theories (CFTs) are special quantum field theories (QFTs) with extra spacetime symmetries. Amongst other things, they play an important role in determining the phase diagrams of QFTs and in the study of second-order phase transitions in condensed matter physics. The extra spacetime symmetries of CFTs lead to an algebra of operators dictated by the operator product expansion (OPE). Contrary to QFTs where perturbation theory is often the only computational handle available, the existence of OPEs allows a specific understanding of CFTs through consistency conditions of correlation functions, even at strong coupling. In this talk we review conformal field theory and discuss the embedding space point of view. Contrary to position space where the conformal algebra action on fields is complicated, the conformal algebra action in embedding space is homogeneous and thus simpler. The use of embedding space allows an easier computation of the correlation functions and the associated conformal blocks from the OPEs in embedding space. The most general function appearing in the conformal blocks is obtained in terms of infinite sums on the conformal cross ratios. Several interesting properties of this function are found and it is shown that it is invariant under the dihedral group of order 12.