Recent Results on the Abelian Projection of Lattice Gluodynamics

We do not have much intuition in nonabelian theories, whereas our understanding of the Maxwell equations and abelian theories is far better. For this reason people are trying to explain the confinement phenomenon in terms of the abelian projection of nonabelian theory [1]. Different abelian projections lead to different abelian theories, and now it is clear that there exist at least one abelian projection, called the maximal abelian projection (MA) [2], in which the resulting abelian theory is close to the dual Abelian Higgs model, the abelian monopoles are condensed and the linear q − q̄ potential can be explained [3] at the level of the classical equations of motion (formation of the dual Abrikosov vortex). The dependence of the abelian theory on the type of the projection is a weak point of this approach, and the popular idea is that all abelian projections can lead to the same physics, if we consider a certain generalized version of the abelian projection, e.g. extended monopoles. Most of the numerical results are obtained in the MA projection which, for the SU(2) gauge theory, corresponds to the minimization of the functional: