Renormalizable Abelian-projected effective gauge theory derived from Quantum Chromodynamics

TL;DR

This paper derives a renormalizable effective Abelian gauge theory from QCD in the maximal Abelian gauge, preserving key features like the beta function and enabling electric-magnetic duality.

Contribution

It systematically improves previous Abelian-projected theories, demonstrating the preservation of the original QCD beta function and enabling dual descriptions.

Findings

Effective coupling's beta function matches that of original QCD.

The theory's anomalous dimensions are explicitly evaluated.

Switching parameters yields electric or magnetic dual theories.

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 in a systematic manner the previous version that was obtained by one of the authors and was referred to as the Abelian-projected effective gauge theory. This result supports the 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 a renormalization-scale dependence governed by the $\beta$-function that is exactly the same as that of 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. Moreover, we evaluate the anomalous dimensions of the fields and parameters in the resultant theory. By choosing the renormalized parameters appropriately, we can switch the theory into an electric or a magnetic theory.