Quantum Mechanics of the Vacuum State in Two-Dimensional QCD with Adjoint Fermions

Abstract

A study of two-dimensional QCD on a spatial circle with Majorana fermions in the adjoint representation of the gauge groups SU(2) and SU(3) has been performed. The main emphasis is put on the symmetry properties related to the homotopically non-trivial gauge transformations and the discrete axial symmetry of this model. Within a gauge fixed canonical framework, the delicate interplay of topology on the one hand and Jacobians and boundary conditions arising in the course of resolving Gauss's law on the other hand is exhibited. As a result, a consistent description of the residual $Z_N$ gauge symmetry (for SU(N)) and the ``axial anomaly" emerges. For illustrative purposes, the vacuum of the model is determined analytically in the limit of a small circle. There, the Born-Oppenheimer approximation is justified and reduces the vacuum problem to simple quantum mechanics. The issue of fermion condensates is addressed and residual discrepancies with other approaches are pointed out.

44 pages; for hardcopies of figures, contact [email protected]

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• Overlap formulation of Majorana--Weyl fermions
• Nonperturbative renormalization and the electron's anomalous moment in large-alpha QED
• SDLCQ: Supersymmetric Discrete Light Cone Quantization
• Adjoint Majorana QCD${}_2$ at Finite $N$
• Vacuum Structure and $\theta$ States of Adjoint QCD in Two Dimensions
• Two dimensional QCD with matter in adjoint representation: What does it teach us?
• Volume dependence of two-dimensional large-N QCD with a nonzero density of baryons
• The Light-Cone Vacuum in 1+1 Dimensional Super-Yang-Mills Theory
• Diffusion of Wilson Loops
• Charge Screening and Confinement in Hot 3-D QED
• On Zero Modes and the Vacuum Problem -- A Study of Scalar Adjoint Matter in Two-Dimensional Yang-Mills Theory via Light-Cone Quantisation
• (1+1)-Dimensional Yang-Mills Theory Coupled to Adjoint Fermions on the Light Front
• Light-Front QCD(1+1) Coupled to Adjoint Scalar Matter
• Light-Front QCD(1+1) Coupled to Chiral Adjoint Fermions
• Four-fermion deformations of the massless Schwinger model and confinement
• Polyakov Loop Dynamics in the Center Symmetric Phase
• Condensates and Vacuum Structure of Adjoint QCD_2
• Polyakov-Loops and Fermionic Zero Modes in QCD2 on the Torus
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• Quantum Electrodynamics in the Light-Front Weyl Gauge
• 2d QCD and Integrability, Part I: 't Hooft model
• A comment on instantons and their fermion zero modes in adjoint QCD_2
• Decompactification of space or time in large N QCD_2
• Vacuum Structure of Two-Dimensional Gauge Theories for Arbitrary Lie Groups
• Vacuum Structures of Supersymmetric Yang-Mills Theories in $1+1$ Dimensions
• Critical Correlations of Wilson Lines in SU(3) and the High Energy ${\gamma }^{\ast }p$ Cross Section
• Universal Deformations
• QCD_{1+1} with Static Quarks as Supersymmetric Quantum Mechanics
• Adjoint $QC{D}_{1+1}$ in Light-cone Gauge, Quantized at Equal Time