Renormalizable Abelian-projected effective gauge theory derived from Quantum Chromodynamics II

TL;DR

This paper extends previous work by proving the multiplicative renormalizability of off-diagonal gluon propagators in an Abelian-projected gauge theory derived from QCD, and calculates key renormalization group functions.

Contribution

It demonstrates the multiplicative renormalizability of off-diagonal gluon Green's functions and computes their anomalous dimensions and renormalization group functions.

Findings

Renormalizability of off-diagonal gluon propagators confirmed

Anomalous dimensions and RG functions calculated

Complements previous results on diagonal gluon and tensor fields

Abstract

In the previous paper\cite{KS00b}, we derived the Abelian projected effective gauge theory as a low energy effective theory of the SU(N) Yang-Mills theory by adopting the maximal Abelian gauge. At that time, we have demonstrated the multiplicative renormalizability of the propagators for the diagonal gluon and the dual Abelian anti-symmetric tensor field. In this paper, we show the multiplicative renormalizability of the Green's functions also for the off-diagonal gluon. Moreover we complement the previous results by calculating the anomalous dimension and the renormalization group functions which are undetermined in the previous paper.