The soft Pomeron from AdS-CFT

Abstract

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 $Ad{S}_5$ is supplemented by a 5d space $X_5$ of effective ``average'' size much larger than the scale of $Ad{S}_5$, 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 $Ad{S}_{d+1}\times X_{\bar{d}}$ 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 $N_c^2{M}_{1,glueball}\sim 10GeV$. Experimentally, one found the ``soft Pomeron'' behaviour, ${\sigma }_{tot}\sim s^{0.093(2)}$, that onsets at about $9GeV$, 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.

19 pages, latex, references added, typos corrected

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• More on Heisenberg's model for high energy nucleon-nucleon scattering
• High Energy Scattering in the AdS/CFT Correspondence
• Scaling Phenomena in Gravity from QCD
• More on the RHIC fireball and dual black holes
• Four point function of R-currents in N=4 SYM in the Regge limit at weak coupling
• Diffractive Vector Meson Photoproduction from Dual String Theory
• A "black hole" solution of scalar field theory