Exact symmetries and threshold states in two-dimensional models for QCD

A bstract Two-dimensional SU( N ) gauge theory coupled to a Majorana fermion in the adjoint representation is nice toy model for higher-dimensional dynamics. It possesses multitude of “gluinoball” bound states whose spectrum has been studied using numerical diagonalizations light-cone Hamiltonian. We extend this by coupling it f flavors fundamental Dirac fermions (quarks). The extended also contains meson-like states, both bosonic and fermionic, which large- limit decouple from gluinoballs. study meson Discretized Light-Cone Quantization (DLCQ). When all are massless, we exhibit an exact $$ \mathfrak{osp} osp (1|4) symmetry algebra that leads infinite number degeneracies DLCQ approach. More generally, show many single-trace threshold degenerate with multi-trace states. These can be explained Kac-Moody current. present strong evidence additional appear continuum limit. Finally, make quarks massive while keeping massless. In case too, observe some mesons becomes continuous above certain threshold. This demonstrates quantitatively string tension vanishes massless QCD 2 without explicit four-fermion operators.