Abelian-projected effective gauge theory of QCD with asymptotic freedom and quark confinement

Abstract

Starting from SU(2) Yang-Mills theory in 3+1 dimensions, we prove that the Abelian-projected effective gauge theories are written in terms of the maximal Abelian gauge field and the dual Abelian gauge field interacting with magnetic monopole current. This is performed by integrating out all the remaining non-Abelian gauge field belonging to SU(2)/U(1). We show that the resulting Abelian gauge theory recovers exactly the same one-loop beta function as the original Yang-Mills theory. Moreover, the dual Abelian gauge field becomes massive if the monopole condensation occurs. This result supports the dual superconductor scenario for quark confinement in QCD. We give a criterion of dual superconductivity and point out that the magnetic monopole condensation may be estimated from the classical instanton configuration. Therefore there can exist an effective Abelian gauge theory which shows both asymptotic freedom and quark confinement based on the dual Meissner mechanism. The inclusion of an arbitrary number of fermion flavors is straightforward in this approach. Some implications to the lower dimensional case will also be discussed.