Gauge invariant eld strength correlators and Abelian dominance in QCD

The QCD infrared dynamics appears to be well approximated by a (dual) Abelian Higgs model [1,2]. Via Abelian projection the QCD gluodynamics is reduced to Abelian elds, Abelian monopoles and charged matter elds degrees of freedom. Then, lattice simulations (mainly in SU(2) and in Maximal Abelian projection) show Abelian dominance and monopole dominance in the long range features of QCD. This means that nonperturbative dynamical quantities like the string tension are reproduced (for more than 90%) simply by considering the Abelian or the monopole degrees of freedom. Moreover, monopoles are condensed in the con ned phase. Electric elds and magnetic currents in the presence of static sources are consistent with the dual Maxwell and Ginzburg{Landau equations. The penetration length = 1=M (M = dual gluon mass) and the correlation length = 1=M (M = Higgs Mass) are measured. Finally, the effective monopole Lagrangian is extracted from an inverse Montecarlo method and turns out to be equivalent to the Lagrangian of the dual Abelian Higgs model. Therefore, the above lattice investigations show that 1) QCD lattice gluodynamics is equivalent to the dual Abelian Higgs model: the Higgs particles are Abelian monopoles and condense in the con nement phase. 2) M 'M and therefore the QCD vacuum behaves as a dual superconductor on the border between type I and type II.