[Paper Review] Abelian Projection of Massive SU(2) Gluodynamics --Towards Color Confinement

Shinichi Deguchi, Yousuke Kokubo|arXiv (Cornell University)|Feb 18, 2003

Particle physics theoretical and experimental studies2 citations

TL;DR

This paper proposes an effective Abelian gauge theory (EAGT) for massive SU(2) gluodynamics to model color confinement, by introducing explicit mass terms for off-diagonal gluons to enforce Abelian dominance at long distances. The EAGT yields a composite potential with Yukawa and linear components, suggesting a mechanism for static quark-antiquark confinement, and is shown to embed the Skyrme-Faddeev model.

ABSTRACT

Towards describing color confinement, we derive an effective Abelian gauge theory (EAGT) of a modified SU(2) gluodynamics. The modification is made by explicitly introducing mass terms of the off-diagonal gluon fields into pure SU(2) gluodynamics, or SU(2) Yang-Mills theory, in order that Abelian dominance at a long-distance scale is realized in SU(2) QCD. In deriving the EAGT, the off-diagonal gluon fields involving longitudinal modes are treated as fields that produce quantum effects on the diagonal gluon field and other fields relevant at a long-distance scale. Unlike earlier papers, a necessary gauge fixing is carried out without spoiling the global SU(2) gauge symmetry. We show that the EAGT allows a composite of the Yukawa and the linear potentials which also occurs in an extended dual Abelian Higgs model. This composite potential is understood to be a static potential between color-electric charges, whose origin may be assigned to the gluon fields. In addition, we point out that the EAGT involves the Skyrme-Faddeev model.

Motivation & Objective

• To develop a framework for understanding color confinement in SU(2) QCD by modifying pure Yang-Mills theory with explicit mass terms for off-diagonal gluons.
• To establish Abelian dominance at long distances in a way that preserves global SU(2) gauge symmetry during gauge fixing.
• To derive an effective Abelian gauge theory (EAGT) that captures long-distance dynamics of massive gluons and their quantum effects.
• To identify the origin of a composite static potential with Yukawa and linear components in the EAGT, linking it to gluonic degrees of freedom.
• To explore connections between the EAGT and the Skyrme-Faddeev model, suggesting deeper topological structure in confinement mechanisms.

Proposed method

• Introduces explicit mass terms for off-diagonal gluon fields in SU(2) Yang-Mills theory to break the off-diagonal gauge symmetry and enable long-distance Abelian dominance.
• Treats the massive off-diagonal gluons as quantum fields that generate effective interactions on the diagonal gluon and long-distance fields.
• Applies a gauge-fixing procedure that preserves the global SU(2) symmetry, avoiding the issues of local symmetry breaking common in earlier approaches.
• Derives the effective Abelian gauge theory (EAGT) by integrating out the massive off-diagonal modes, resulting in a low-energy effective action.
• Analyzes the resulting EAGT to identify the form of the static potential between color-electric charges, showing a composite of Yukawa and linear terms.
• Identifies structural similarities between the EAGT and the Skyrme-Faddeev model, indicating possible topological soliton solutions.

Experimental results

Research questions

• RQ1 Can explicit mass terms for off-diagonal gluons in SU(2) Yang-Mills theory lead to Abelian dominance at long distances?
• RQ2 How can gauge fixing be performed without breaking global SU(2) symmetry while deriving an effective Abelian theory?
• RQ3 What form does the static potential between color-electric charges take in the derived EAGT, and what is its physical origin?
• RQ4 Does the EAGT exhibit structural or dynamical similarities with the Skyrme-Faddeev model?
• RQ5 Can the composite potential in the EAGT account for features of quark confinement, such as linear and Yukawa-like behavior?

Key findings

• The effective Abelian gauge theory (EAGT) successfully realizes Abelian dominance at long distances in massive SU(2) gluodynamics through explicit off-diagonal gluon mass terms.
• The EAGT generates a composite static potential with both Yukawa and linear components, characteristic of confinement mechanisms.
• This composite potential arises from the quantum effects of massive off-diagonal gluons on the diagonal gluon sector and is interpreted as a static interaction between color-electric charges.
• The EAGT is shown to contain the structure of the Skyrme-Faddeev model, suggesting possible topological soliton solutions relevant to confinement.
• The gauge-fixing procedure preserves global SU(2) symmetry, resolving a key limitation of earlier approaches to Abelian projection.
• The results support the idea that gluonic degrees of freedom, particularly massive off-diagonal modes, can mediate a confining potential in non-Abelian gauge theories.