VACUUM-STRUCTURE OF 2-DIMENSIONAL GAUGE-THEORIES ON THE LIGHT-FRONT

We discuss the problem of vacuum structure in light-front field theory in the context of (1+1)-dimensional gauge theories. We begin by revie wing the known light-front solution of the Schwinger model, highlighti ng the issues that are relevant for reproducing the theta structure of the vacuum. The most important of these are the need to introduce deg rees of freedom initialized on two different null planes, the proper i ncorporation of gauge field zero modes when periodicity conditions are used to regulate the infrared, and the importance of carefully regula ting singular operator products in a gauge-invariant way. We then cons ider SU(2) Yang-Mills theory in 1+1 dimensions coupled to massless adj oint 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 m odel using periodicity conditions in x(+/-) for infrared regulation, a nd consider a solution in which the gauge field zero mode is treated a s 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 condensat e, which is sensitive to the vacuum structure. The result is nonzero, but inversely proportional to the periodicity length, a situation whic h is familiar from the Schwinger model. The origin of this behavior is discussed.