The soft Pomeron from AdS-CFT

In previous treatments, high energy QCD was analyzed using AdS-CFT a la Polchinski-Strassler. Black hole production in AdS was responsible for power law behaviour of the total QCD cross section. Using the simplest self-consistent gravity dual assumption, that cut-off $AdS_5$ is supplemented by a 5d space $X_5$ of effective ``average'' size much larger than the scale of $AdS_5$, we find an energy behaviour just before the saturation of the Froissart bound that is $\sigma_{tot} \sim s^{1/n}= s^{1/11}\simeq s^{0.0909}$. It comes from the solution of the Laplacean on $AdS_{d+1}\times X_{\bar{d}}$ behaving like $1/r^n=1/r^{2(d-1)+\bar{d}}= 1/r^{11}$. We argue that this should be present in real QCD as well, as string corrections to the dual scattering are small, and should onset at about $N_c^2 M_{1, glueball}\sim 10 GeV$. Experimentally, one found the ``soft Pomeron'' behaviour, $\sigma_{tot}\sim s^{0.093(2)}$, that onsets at about $ 9 GeV$, that was later argued to be replaced by the unitarized Froissart + reaction-dependent constant behaviour. We argue that the soft Pomeron and the dual behaviour represent the same physics, creation of an effective field theory ``soliton''-like structure (=black hole), that then decays, and so they have to be taken seriously. We thus have an experimental prediction of string theory, literally counting the extra dimensions.