  Recently, sum rules were derived for the inverse eigenvalues of the Dirac
operator. They were obtained in two different ways: i) starting from the
low-energy effective Lagrangian and ii) starting from a random matrix theory
with the symmetries of the Dirac operator. This suggests that the effective
theory can be obtained directly from the random matrix theory. Previously, this
was shown for three or more colors with fundamental fermions. In this paper we
construct the effective theory from a random matrix theory for two colors in
the fundamental representation and for an arbitrary number of colors in the
adjoint representation. We construct a fermionic partition function for
Majorana fermions in Euclidean space time. Their reality condition is
formulated in terms of complex conjugation of the second kind.
