  In this paper we construct a model that satisfies the theoretical requisites
of high energy soft interactions, based on two ingredients:(i) the results of
N=4 SYM, which at present is a unique theory that allows one to deal with a
large coupling constant; and (ii) the requirement of matching with high energy
QCD. In accordance with these ideas, we assume that the soft Pomeron intercept
is rather large, and the slope of the Pomeron trajectory is equal to zero. We
derive analytical formulae that sum both enhanced and semi-enhanced diagrams
for elastic and diffractive amplitudes. We fit the available experimental data,
and predict the valuefor cross sections at the energies accessible at the LHC.
The main corrections to the model are studied and evaluated.
