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

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)/Z 2 , 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 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 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.

Localisation in worldline pair production and lightfront zero-modes

“…It was shown in [18,19] that standard regularisations of zero-modes would imply that there is no pair production in fields E 3 (x + ), contradicting the constant field results of [2,3]. This problem was solved in [18,19] by quantising on two lightlike hypersurfaces, one of fixed x + and one of fixed x − = x 0 − x 3 [24,25]. Although effectively abandoning the usual lightfront approach, this allowed control of the zero-modes and lead to a nonzero pair production probability (which was also recovered from a functional computation of…”

On the spectrum of(1+1)-dimensional QCD withSU(Nc)

“…The massive spectrum is not affected by this omission [21]. We use the convenient Dirac basis γ 0 = σ 1 , γ 1 = −iσ 2 .…”

Bound states of dimensionally reduced SYM2+1 at finite N

“…An interpretation of the matrix model for M(atrix) Theory at finite N has also been given by Susskind [9], providing additional motivation to study super Yang-Mills at finite N. We should stress, however, that in the model we study here, we compactify the null direction x − , rather than in a spatial direction. Furthermore, we drop the zero mode sector [14,15], which is conventional in DLCQ, and therefore we eliminate any possibility of connecting our solutions with an equal time quantization of the same theory with a spatially compactified dimension. However, experience with DLCQ has shown that the massive spectrum is insensitive to how the theory is compactified, and to the zero modes.…”