## Zero modes and the vacuum problem: A study of scalar adjoint matter in two-dimensional Yang-Mills theory via light-cone quantization

SU(2) Yang-Mills theory coupled to massive adjoint scalar matter is studied in 1+1 dimensions using discretized light-cone quantization. This theory can be obtained from pure Yang-Mills theory in 2+1 dimensions via dimensional reduction. On the light cone, the vacuum structure of this theory is encoded in the dynamical zero mode of a gluon and a constrained mode of the scalar field. The latter satisfies a linear constraint, suggesting no nontrivial vacua in the present paradigm for symmetry breaking on the light cone. I develop a diagrammatic method to solve the constraint equation. In the adiabatic approximation I compute the quantum-mechanicalmore »