Vacuum Structure of Two-Dimensional Gauge Theories on the Light Front

Abstract

We discuss the problem of vacuum structure in light-front field theory in the context of (1+1)-dimensional gauge theories. We begin by reviewing the known light-front solution of the Schwinger model, highlighting the issues that are relevant for reproducing the $\theta$-structure of the vacuum. The most important of these are the need to introduce degrees of freedom initialized on two different null planes, the proper incorporation of gauge field zero modes when periodicity conditions are used to regulate the infrared, and the importance of carefully regulating singular operator products in a gauge-invariant way. We then consider SU(2) Yang-Mills theory in 1+1 dimensions coupled to massless adjoint fermions. With all fields in the adjoint representation the gauge group is actually SU(2)$/Z_2$, which possesses nontrivial topology. In particular, there are two topological sectors and the physical vacuum state has a structure analogous to a $\theta$ vacuum. We formulate the model using periodicity conditions in $x^{\pm }$ for infrared regulation, and consider a solution in which the gauge field zero mode is treated as a constrained operator. We obtain the expected $Z_2$ vacuum structure, and verify that the discrete vacuum angle which enters has no effect on the spectrum of the theory. We then calculate the chiral condensate, which is sensitive to the vacuum structure. The result is nonzero, but inversely proportional to the periodicity length, a situation which is familiar from the Schwinger model. The origin of this behavior is discussed.

29 pages, uses RevTeX. Improved discussion of the physical subspace generally and the vacuum states in particular. Basic conclusions are unchanged, but some specific results are modified

References in corpus (2)

• Vacuum Structure and $\theta$ States of Adjoint QCD in Two Dimensions
• Some Lessons from the Schwinger Model

Cited by in corpus (21)

• Quantum Chromodynamics and Other Field Theories on the Light Cone
• Anomalies, a mod 2 index, and dynamics of 2d adjoint QCD
• Nonperturbative light-front Hamiltonian methods
• On the Transition from Confinement to Screening in QCD_{1+1} Coupled to Adjoint Fermions at Finite N
• Non-Perturbative Spectrum of Two Dimensional (1,1) Super Yang-Mills at Finite and Large N
• SDLCQ: Supersymmetric Discrete Light Cone Quantization
• DLCQ Bound States of N =(2,2) Super-Yang-Mills at Finite and Large N
• The DLCQ Spectrum of N=(8,8) Super Yang-Mills
• The Light-Cone Vacuum in 1+1 Dimensional Super-Yang-Mills Theory
• On the Spectrum of QCD(1+1) with SU(N_c) Currents
• (1+1)-Dimensional Yang-Mills Theory Coupled to Adjoint Fermions on the Light Front
• Variational Mass Perturbation Theory for Light-Front Bound-State Equations
• Theta-Vacuum of the Bosonized Massive Light-Front Schwinger Model
• Condensates and Vacuum Structure of Adjoint QCD_2
• Scattering in strong electromagnetic fields: transverse size effects in tBLFQ
• Effect of Zero Modes on the Bound-State Spectrum in Light-Cone Quantisation
• Spontaneously broken quark helicity symmetry
• Vacuum Structure of Two-Dimensional Gauge Theories for Arbitrary Lie Groups
• Light-Cone Quantization and Renormalization of Large-N Scalar Matrix Models
• Universal Deformations
• Adjoint $QC{D}_{1+1}$ in Light-cone Gauge, Quantized at Equal Time