Conformal bootstrap in Mellin space from GG systems

Abstract

A simple scheme to express the Mellin transform of $D$-dimensional Euclidean conformal bootstrap equation is presented by relating conformal blocks to a Gauss-Grassmann (GG) system due to Gelfand-Graev, associated to conformal integrals, which, in turn, are generalised hypergeometric functions. Usefulness of the expression for obtaining bounds on the spectrum of fields is demonstrated.

9 pages, 2 figures. References added. Some explanatory remarks on the connection to the GKZ system and independence on the ${\hat{I}}^2$ parameters added. Version to appear in Phys Lett B