Renormalizable Abelian-projected effective gauge theory derived from Quantum Chromodynamics

Abstract We show that an effective Abelian gauge theory can be obtained as a renormalizable theory from QCD in the maximal Abelian gauge. The derivation improves the previous version which was obtained by one of the authors and was called the Abelianprojected effective gauge theory. This result supports a view that we can construct an effective Abelian gauge theory from QCD without losing characteristic features of the original non-Abelian gauge theory. In fact, it is shown that the effective coupling constant in the resulting renormalizable theory has the renormalization-scale dependence governed by the β-function which is exactly the same as the original Yang-Mills theory (irrespective of the choice of gauge fixing parameters of the maximal Abelian gauge and the parameters used for identifying the dual variables). By choosing the renormalized parameters appropriately, we can switch the theory into the electric or magnetic theory.