Critical correlations of Wilson lines in SU(3) and the high energy γ*p cross section -: art. no. 034020

We discuss deep inelastic scattering at high energies as a critical phenomenon in 2+1 space-time dimensions. In the limit of Bjorken x-->0, QCD SU(3) with quark fields becomes a critical theory with a diverging correlation length xi(x)proportional tox(2)(-1/2lambda) where the exponent lambda(2)=2.52 is obtained from the center group Z(3) of SU(3). We conjecture that the dipole wave function of the virtual photon for transverse sizes 1/Q<x(perpendicular to)<xi obeys a correlation scaling Psiproportional to(x(perpendicular to))(-(1+n)) before exponentially decaying for distances larger than the correlation length. Using this behavior combined with different x-independent dipole proton cross sections we calculate the proton structure function and compare it with the experimental data. We take the good agreement with the measured proton structure function F-2(x,Q(2)) as an indication that at high energies dimensional reduction to an effective three dimensional theory with a critical point occurs.