Dual Shapiro-Virasoro amplitudes in the QCD dipole picture

Using the QCD dipole picture of BFKL dynamics and the conformal invariance properties of the BFKL kernel in transverse coordinate space, we show that the 1--to--p dipole densities can be expressed in terms of dual Shapiro- Virasoro amplitudes B{2p+2} and their generalization including non-zero conformal spins. We discuss the possibility of an effective closed string theory of interacting QCD dipoles.