Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1997-09-16
Phys.Rev. D57 (1998) 7467-7487
Physics
High Energy Physics
High Energy Physics - Theory
39 pages, Latex, no figures, (2.2, 4.1, 4.3 are modified; 4.4, Appendices A,B,C and references are added. No change in conclus
Scientific paper
10.1103/PhysRevD.57.7467
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 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 monopole condensation can be estimated from the classical instanton configuration. Therefore there can exist the effective abelian gauge theory which shows both asymptotic freedom and quark confinement based on the dual Meissner mechanism. Inclusion of arbitrary number of fermion flavors is straightforward in this approach. Some implications to lower dimensional case will also be discussed.
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