Ginzburg - Landau equation from SU(2) gauge field theory

TL;DR

This paper derives a Ginzburg-Landau-like equation from pure SU(2) gauge theory using Abelian projection, linking it to the dual superconductor model of the QCD vacuum and confinement.

Contribution

It demonstrates how a GL-like equation with spontaneous symmetry breaking can be obtained directly from SU(2) gauge fields via Abelian projection and ghost field condensation.

Findings

Derived a GL-like equation from SU(2) gauge theory.

Connected the model to the dual superconductor picture of QCD.

Showed the emergence of a tachyonic mass from ghost condensation.

Abstract

The dual superconductor picture of the QCD vacuum is thought to describe various aspects of the strong interaction including confinement. Ordinary superconductivity is described by the Ginzburg-Landau (GL) equation. In the present work we show that it is possible to arrive at a GL-like equation from pure SU(2) gauge theory. This is accomplished by using Abelian projection to split the SU(2) gauge fields into an Abelian subgroup and its coset. The two gauge field components of the coset part act as the effective, complex, scalar field of the GL equation. The Abelian part of the SU(2) gauge field is then analogous to the electromagnetic potential in the GL equation. An important aspect of the dual superconducting model is for the GL Lagrangian to have a spontaneous symmetry breaking potential, and the existence of Nielsen-Olesen flux tube solutions. Both of these require a tachyonic mass for the effective scalar field. Such a tachyonic mass term is obtained from the condensation of ghost fields.