  An effective theory designed to compute Virasoro identity blocks at large
central charge, expressed in terms of the propagation of a
reparametrization/shadow mode between bilocal vertices, was recently put
forward. In this paper I provide the formal theoretical framework underlying
this effective theory by reformulating it in terms of standard concepts :
conformal geometry, generating functionals and Feynman diagrams. A key
ingredient to this formalism is the bilocal vertex operator, or reparametrized
two-point function, which is shown to generate arbitrary stress tensor
insertions into a two-point function of reference. I also suggest an extension
of the formalism designed to compute generic Virasoro blocks.
