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The spectra of two-dimensional $su(2)$ gauge theories coupled to a singlemassless Majorana fermion in integer representations, $J$, are numericallyinvestigated using the Discrete Light-Cone Hamiltonian. One of our aims is toexplore the possible presence of massless states for $J>2$ in spite of theabsence of a continuous symmetry. After comparing to existing results for $J=1$(adjoint fermions), we present results for $J=2,3,4$. As expected, for $J=2$there are no massless states but in contrast to the $J=1$ theory, the lighteststate is a boson. We find exact massless modes in the bosonic and fermionicsector for all values of total momentum for $J=3$ and $J=4$ and, in eachsector, the number of massless modes grows with the value of the totalmomentum. In addition to the spectrum, we present results on the particlenumber and momentum fraction distributions and argue for a separation of bulkstates from edge states.

Spectrum of two-dimensional $su(2)$ gauge theories coupled to massless fermions in integer representations