(1+1)-Dimensional Yang-Mills Theory Coupled to Adjoint Fermions on the Light Front

TL;DR

This paper studies 1+1 dimensional SU(2) Yang-Mills theory with adjoint fermions on the light front, revealing topological vacuum structures, constructing the  vacuum, and analyzing the fermion condensate's role in the spectrum and string tension.

Contribution

It demonstrates how to realize the  vacuum structure in light-front quantization and explores the condensate's impact on the theory's spectrum and confinement.

Findings

Identification of degenerate vacuum states and  vacuum construction.

The fermion condensate does not alter the spectrum.

The condensate relates to string tension but does not affect the spectrum.

Abstract

We 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 distinct topological sectors and the physical vacuum state has a structure analogous to a \theta vacuum. We show how this feature is realized in light-front quantization, with periodicity conditions used to regulate the infrared and treating the gauge field zero mode as a dynamical quantity. We find expressions for the degenerate vacuum states and construct the analog of the \theta vacuum. We then calculate the bilinear condensate in the model. We argue that the condensate does not affect the spectrum of the theory, although it is related to the string tension that characterizes the potential between fundamental test charges when the dynamical fermions are given a mass. We also argue that this result is fundamentally different from calculations that use periodicity conditions in x^1 as an infrared regulator.