Is QCD at small x a string theory?

Using the dipole picture describing the $1\mathrm{/}{N}_C$ 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 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.