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We discuss deep inelastic scattering at high energies as a criticalphenomenon in 2+1 space - time dimensions. In the limit of Bjorken $x \to 0$,$QCD$ SU(3) with quark fields becomes a critical theory with a divergingcorrelation length $\xi(x) \propto x^{-\frac{1}{2 \lambda_2}}$ where theexponent $\lambda_2=2.52$ is obtained from the center group Z(3) of SU(3). Weconjecture that the dipole wave function of the virtual photon for transversesizes $1/Q<x_{\bot}<\xi$ obeys correlation scaling $\Psi \propto(x_{\bot})^{-(1+n)}$ before exponentially decaying for distances larger thanthe correlation length. Using this behavior combined with different $x$-independent dipole proton cross sections we calculate the proton structurefunction and compare with the experimental data. We take the good agreementwith the measured proton structure function F$_2(x,Q^2)$ as an indication thatat high energies dimensional reduction to an effective three dimensional theorywith a critical point occurs.Comment: 21 pages, 3 figure

physical review. d. particles, fields, gravitation, and cosmology/physical review. d. particles and fields

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Critical correlations of Wilson lines in SU(3) and the high energyγ*pcross section