Using the dipole picture describing the 1/N-C limit of QCD at small x
and the conformal invariance properties of the BFKL kernel in transver
se coordinate space, we show that the 1 double right arrow p dipole de
nsities can be expressed in terms of dual Shapiro-Virasoro amplitudes
B2p+2 and their generalization including non-zero conformal spins. We
discuss the possibility of an effective closed string theory of intera
cting QCD dipoles. (C) 1997 Published by Elsevier Science B.V.