Model for SU(3) vacuum degeneracy using light-cone coordinates

TL;DR

This paper develops a light-cone coordinate model for the SU(3) gauge theory in 2+1 dimensions, analyzing zero-modes and vacuum structure through dimensional reduction and quantization, revealing a non-degenerate vacuum under certain conditions.

Contribution

It introduces a novel approach to study SU(3) vacuum degeneracy using light-cone coordinates and zero-mode analysis in a reduced 1+1 dimensional framework.

Findings

Vacuum is non-degenerate when constrained zero-modes are neglected.

Derived a Schrödinger equation linking dynamical zero-modes to the vacuum.

Provided a new perspective on SU(3) vacuum structure in lower dimensions.

Abstract

Working in light-cone coordinates, we study the zero-modes and the vacuum in a 2+1 dimensional SU(3) gauge model. Considering the fields as independent of the tranverse variables, we dimensionally reduce this model to 1+1 dimensions. After introducing an appropriate su(3) basis and gauge conditions, we extract an adjoint field from the model. Quantization of this adjoint field and field equations lead to two constrained and two dynamical zero-modes. We link the dynamical zero-modes to the vacuum by writing down a Schrodinger equation and prove the non-degeneracy of the SU(3) vacuum provided that we neglect the contribution of constrained zero-modes.