  Two-dimensional SU$(N)$ gauge theory coupled to a Majorana fermion in the
adjoint representation is a nice toy model for higher-dimensional gauge
dynamics. It possesses a multitude of "gluinoball" bound states whose spectrum
has been studied using numerical diagonalizations of the light-cone
Hamiltonian. We extend this model by coupling it to $N_f$ flavors of
fundamental Dirac fermions (quarks). The extended model also contains
meson-like bound states, both bosonic and fermionic, which in the large-$N$
limit decouple from the gluinoballs. We study the large-$N$ meson spectrum
using the Discretized Light-Cone Quantization (DLCQ). When all the fermions are
massless, we exhibit an exact $\mathfrak{osp}(1|4)$ symmetry algebra that leads
to an infinite number of degeneracies in the DLCQ approach. More generally, we
show that many single-trace states in the theory are threshold bound states
that are degenerate with multi-trace states. These exact degeneracies can be
explained using the Kac-Moody algebra of the SU$(N)$ current. We also present
strong numerical evidence that additional threshold states appear in the
continuum limit. Finally, we make the quarks massive while keeping the adjoint
fermion massless. In this case too, we observe some exact degeneracies that
show that the spectrum of mesons becomes continuous above a certain threshold.
This demonstrates quantitatively that the fundamental string tension vanishes
in the massless adjoint QCD$_2$.
