(1+1)-dimensional Yang-Mills theory coupled to adjoint fermions on the light front

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 θ vacuum. We show how this feature is realized in light-front quantization, with periodicity conditions in x ± 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 θ 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.

SDLCQ supersymmetric discrete light cone quantization

“…As we saw in the previous subsection supersymmetry leads to the cancellation of the anomaly terms in current operator. However these terms played an important role in the description of Z N degeneracy of vacua [70], so we should find another explanation of this fact here. It appears that fermionic zero modes give a natural framework for such treatment.…”

“…The explicit form of T depends on the rank of the group, for SU(2) and SU(3) it may be found in [59]. The operator S satisfies the condition S N = 1 and it was used in classifying the vacua [59,70].…”

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.…”

“…Schematically, the general structure of an arbitrary Fock state with k traces has the form 14) where n denotes the total number of partons in each Fock state, and the integers i 1 , i 2 , . .…”