1+1d QCD with Quarks and Adjoint Fermions at Finite N

Abstract

Despite theories of quantum chromodynamics (QCD) dating back to the 1970s and decades of experimental work verifying that QCD is the correct high-energy description of the strong nuclear force, the dynamics of how quarks and gluons give rise to hadrons in the low-energy limit has only partially been solved. This is due to the non-perturbative nature of QCD, which prevents a complete analytic solution, giving rise to confinement: the phenomenon that all bound hadrons come in color-neutral states. One method researchers have used to understand this is to consider the theory in 1+1 dimensions, rather than the usual 3+1. Here, the gluon becomes non-dynamical. To restore some of the dynamics the gluon had, a new particle, the Majorana adjoint fermion, is added. A recent paper by Dempsey et al., showed that this theory may be solved numerically in the case of a finite number of colors and only adjoint fermions. Another paper by Kent Hornbostel showed that this theory may be solved in the case of purely quarks. This paper aims to solve the wider theory with both adjoint fermions and quarks at a finite number of colors. In doing so, we are able to compare our results with both Hornbostel and Dempsey. Finally, we build off of their work by solving the theory for mesons and baryons with both quarks and adjoint fermions, and discuss the implications of our results in the conclusion.