  We analyze Dirac spectra of two-dimensional QCD like theories both in the
continuum and on the lattice and classify them according to random matrix
theories sharing the same global symmetries. The classification is different
from QCD in four dimensions because the anti-unitary symmetries do not commute
with $\gamma_5$. Therefore in a chiral basis, the number of degrees of freedom
per matrix element are not given by the Dyson index. Our predictions are
confirmed by Dirac spectra from quenched lattice simulations for QCD with two
or three colors with quarks in the fundamental representation as well as in the
adjoint representation. The universality class of the spectra depends on the
parity of the number of lattice points in each direction. Our results show an
agreement with random matrix theory that is qualitatively similar to the
agreement found for QCD in four dimensions. We discuss the implications for the
Mermin-Wagner-Coleman theorem and put our results in the context of
two-dimensional disordered systems.
