Gluon saturation and black hole criticality

We discuss the recent proposal [1] where it was shown that the critical anomalous dimension associated to the onset of non.linear effects in the high energy limit of QCD coincides with the critical exponent governing the radius of the black hole formed in the spherically symmetric collapse of a massless scalar field. We argue that a new essential ingredient in this mapping between gauge theory and gravity is continuous self-similarity, not present in the scalar field case but in the spherical collapse of a perfect fluid with barotropic equation of state. We identify this property with geometric scaling, present in DIS data at small values of Bjorken x. We also show that the Choptuik exponent in dimension five tends to the QCD critical value in the traceless limit of the energy momentum tensor.