[Paper Review] Dyons in QCD: Confinement and Chiral Symmetry Breaking

Yu. A. Simonov|ArXiv.org|Sep 27, 1995

Quantum Chromodynamics and Particle Interactions3 citations

TL;DR

This paper proposes a dyon gas model in SU(2) gluodynamics to explain confinement and chiral symmetry breaking in QCD. It derives exact dyonic solutions in various gauges, analyzes their classical interactions, demonstrates confinement via topological properties, and shows chiral symmetry breaking through fermionic zero modes in the dyon background, providing a unified framework for non-perturbative QCD phenomena.

ABSTRACT

Dyonic classical solutions of $SU(2)$ gluodynamics are discussed. Exact form of dyonic solutions in different gauges is presented and the nontrivial problem of composition of the dilute gas of dyons is settled. Classical interaction between (anti)dyons is considered both analytically and numerically. Confinement in the dyonic gas is discussed in connection with the topological properties of individual dyon solution. Fermionic zero modes of dyonic are displayed and the chiral symmetry breaking in the dyonic gas is demonstrated.

Motivation & Objective

• To understand the role of dyons in non-perturbative QCD phenomena such as confinement and chiral symmetry breaking.
• To construct exact classical solutions for dyons in SU(2) gluodynamics across different gauges.
• To analyze the dilute gas approximation of dyons and their classical interactions analytically and numerically.
• To link confinement to the topological structure of individual dyon solutions.
• To demonstrate chiral symmetry breaking via the existence of fermionic zero modes in the dyon background.

Proposed method

• Derives exact classical solutions for dyons in SU(2) Yang-Mills theory using various gauge choices.
• Applies the dilute gas approximation to model a system of weakly interacting dyons.
• Computes classical interaction potentials between (anti)dyons using analytical and numerical techniques.
• Examines topological invariants and instanton-like structures in individual dyon solutions to connect to confinement.
• Analyzes the Dirac equation in the dyon background to identify fermionic zero modes.
• Uses the presence of zero modes to infer spontaneous chiral symmetry breaking in the dyonic medium.

Experimental results

Research questions

• RQ1 How do exact dyonic solutions in SU(2) gluodynamics contribute to confinement?
• RQ2 What is the nature of classical interactions between dyons and anti-dyons in different gauges?
• RQ3 How do topological properties of individual dyons lead to confinement in the gas model?
• RQ4 What role do fermionic zero modes play in chiral symmetry breaking within the dyonic medium?
• RQ5 Can the dyon gas model consistently describe both confinement and chiral symmetry breaking in QCD?

Key findings

• Exact classical dyonic solutions are derived in multiple gauges, providing a foundation for studying their dynamics.
• The classical interaction between (anti)dyons is computed analytically and numerically, supporting the dilute gas approximation.
• Confinement is linked to the topological structure of individual dyon solutions, particularly their winding numbers.
• Fermionic zero modes are explicitly found in the dyon background, signaling the breaking of chiral symmetry.
• The presence of zero modes confirms that the dyonic gas phase supports spontaneous chiral symmetry breaking.
• The model provides a unified description of confinement and chiral symmetry breaking via dyonic constituents in QCD.