On Zero Modes and the Vacuum Problem -- A Study of Scalar Adjoint Matter in Two-Dimensional Yang-Mills Theory via Light-Cone Quantisation

Abstract

SU(2) Yang-Mills Theory coupled to massive adjoint scalar matter is studied in (1+1) dimensions using Discretised Light-Cone Quantisation. This theory can be obtained from pure Yang-Mills in 2+1 dimensions via dimensional reduction. On the light-cone, the vacuum structure of this theory is encoded in the dynamical zero mode of a gluon and a constrained mode of the scalar field. The latter satisfies a linear constraint, suggesting no nontrivial vacua in the present paradigm for symmetry breaking on the light-cone. I develop a diagrammatic method to solve the constraint equation. In the adiabatic approximation I compute the quantum mechanical potential governing the dynamical gauge mode. Due to a condensation of the lowest omentum modes of the dynamical gluons, a centrifugal barrier is generated in the adiabatic potential. In the present theory however, the barrier height appears too small to make any impact in this odel. Although the theory is superrenormalisable on naive powercounting grounds, the removal of ultraviolet divergences is nontrivial when the constrained mode is taken into account. The open aspects of this problem are discussed in detail.

LaTeX file, 26 pages. 14 postscript figures

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• SDLCQ: Supersymmetric Discrete Light Cone Quantization
• The Light-Cone Vacuum in 1+1 Dimensional Super-Yang-Mills Theory
• Theta-Vacuum of the Bosonized Massive Light-Front Schwinger Model
• Large Gauge Transformations and the Light-Front Vacuum Structure
• Fermionic Zero Modes and Spontaneous Symmetry Breaking on the Light Front
• Effect of Zero Modes on the Bound-State Spectrum in Light-Cone Quantisation
• Quantum Electrodynamics in the Light-Front Weyl Gauge
• Succesful renormalization of a QCD-inspired Hamiltonian
• Model for SU(3) vacuum degeneracy using light-cone coordinates