Dual Shapiro-Virasoro amplitudes in the dipole picture of QCD at small x

Using the dipole picture describing the 1NC limit of QCD at small x and the conformal invariance properties of the BFKL kernel in transverse coordinate space, we show that the 1 ⇒ p dipole densities 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 interacting QCD dipoles.