  Although QCD can be treated perturbatively in the high energy limit, lower
energies requre uses of nonperturbative methods such as ADS/CFT and/or Abelian
reduction.These methods are not equivalent. In this paper we provide arguments
in favor of the Abelian reduction methods. This is achieved by further
developing results of our recent works reanalyzing Veneziano and Veneziano-like
amplitudes and the models associated with these amplitudes. It is shown, that
the obtained new partition function for these amplitudes can be mapped exactly
into that for the Polychronakos-Frahm spin chain model recoverable from the
Richardson-Gaudin XXX spin chain model used originally for treatments of the
BCS-type superconductivity. Because of this, it is demonstrated that the
obtained mapping is compatible with the method of Abelian reduction.
