Conformal invariance and QCD Pomeron vertices in the 1/N_c limit

Using the dipole framework for QCD at small x in the 1/N_c limit, we derive the expression of the 1 -> p dipole multiplicity density in momentum space. This gives an analytical expression for the 1 -> p QCD Pomeron amplitudes in terms of one-loop integration of effective vertices in transverse momentum. Conformal invariance and a Hilbert space construction for dipole correlation functions are the main tools of the derivation. Relations with conformal field theories in the classical limit are discussed.