Abelian-Projected Effective Gauge Theory of QCD with Asymptotic Freedom and Quark Confinement

TL;DR

This paper derives an abelian-projected effective gauge theory from SU(2) Yang-Mills theory, demonstrating it retains asymptotic freedom and supports quark confinement via monopole condensation, aligning with the dual superconductor model.

Contribution

It provides a rigorous derivation of an abelian gauge theory from SU(2) Yang-Mills that reproduces the one-loop beta function and explains quark confinement through monopole condensation.

Findings

The abelian-projected theory recovers the same one-loop beta function as the original theory.

Monopole condensation leads to a massive dual gauge field, supporting the dual superconductor scenario.

The effective abelian theory exhibits both asymptotic freedom and quark confinement mechanisms.

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 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.