Document Type
Article
Publication Date
7-15-1997
Publication Title
Physical Review D
Publisher
American Physical Society
Keywords
Vacuum Structure, Light-Front Theory, Gauge Theory, Schwinger Model, SU(2) Yang-Mills Theory
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 θ 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)/Z2, which possesses nontrivial topology. In particular, there are two topological sectors and the physical vacuum state has a structure analogous to a θ vacuum. We formulate the model using periodicity conditions in x± for infrared regulation, and consider a solution in which the gauge field zero mode is treated as a constrained operator. We obtain the expected Z2 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.
First Page
1035
Last Page
1049
Volume
56
Issue
2
Repository Citation
McCartor, Gary; Robertson, David G.; and Pinksy, Stephen S., "Vacuum Structure of Two-Dimensional Gauge Theories on the Light Front" (1997). Physics Faculty Scholarship. 14.
https://digitalcommons.otterbein.edu/phys_fac/14
Original Citation
McCartot, G., Robertson, D.G., & Pinsky, S.S. (1997). Vacuum structure of two-dimensional gauge theories on the light front. Physical Review D, 56(2). DOI: 10.1103/PhysRevD.56.1035
DOI
10.1103/PhysRevD.56.1035
Version
Publisher's Version
Publisher's Statement
Copyright 1997 Physical Review D
Peer Reviewed
1
Creative Commons License
This work is licensed under a Creative Commons Attribution 3.0 License.