Compact lattice formulation of Cho-Faddeev-Niemi decomposition: gluon mass generation and infrared Abelian dominance

TL;DR

This paper introduces a new lattice formulation of SU(2) Yang-Mills theory that explains infrared Abelian dominance and gluon mass generation in a gauge-invariant manner, confirmed through numerical simulations.

Contribution

It presents a compact lattice formulation using new variables that naturally explain infrared Abelian dominance and gluon mass generation without gauge fixing.

Findings

Gluon degrees of freedom other than Abelian parts acquire mass and decouple at low energies.

The formulation explains infrared Abelian dominance in a gauge-invariant way.

Numerical simulations support the decoupling of non-Abelian gluons in the infrared.

Abstract

This paper complements a new lattice formulation of SU(2) Yang-Mills theory written in terms of new variables in a compact form proposed in the previous paper. The new variables used in the formulation were once called the Cho--Faddeev--Niemi or Cho--Faddeev--Niemi--Shabanov decomposition. Our formulation enables us to explain the infrared ``Abelian'' dominance, in addition to magnetic monopole dominance shown in the previous paper, in the gauge invariant way without relying on the specific gauge fixing called the maximal Abelian gauge used in the conventional investigations. In this paper, especially, we demonstrate by numerical simulations that gluon degrees of freedom other than the ``Abelian'' part acquire the mass to be decoupled in the low-energy region leading to the infrared Abelian dominance.