Conformal Field Theory in Conformal Space
  We present a new framework for a Lagrangian description of conformal field theories in various dimensions based on a local version of d+2-dimensional conformal space. The results include a true gauge theory of conformal gravity in d=(1,3) and any standard matter coupled to it. An important feature is the automatic derivation of the conformal gravity constraints, which are necessary for the analysis of the matter systems. 
C. R. Preitschopf and M. A. Vasiliev