Vacuum structure of two-dimensional gauge theories on the light front

Journal Article · Tue Jul 01 04:00:00 EDT 1997 · Physical Review, D

DOI:https://doi.org/10.1103/PhysRevD.56.1035· OSTI ID:527083

McCartor, G ^[1]; Robertson, D G; Pinsky, S S ^[2]

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1. Department of Physics, Southern Methodist University, Dallas, Texas 75275 (United States)
2. Department of Physics, The Ohio State University, Columbus, Ohio 43210 (United States)

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{sub 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{sup {plus_minus}} 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{sub 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. {copyright} {ital 1997} {ital The American Physical Society}

• OSTI ID: 527083
• Journal Information: Physical Review, D, Journal Name: Physical Review, D Journal Issue: 2 Vol. 56; ISSN PRVDAQ; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

66 PHYSICS
GAUGE INVARIANCE
LIGHT CONE
MASSLESS PARTICLES
QUANTUM FIELD THEORY
SU-2 GROUPS
TOPOLOGY
TWO-DIMENSIONAL CALCULATIONS
UNIFIED GAUGE MODELS
VACUUM STATES
YANG-MILLS THEORY