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

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.

Included in

Physics Commons

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