The orthogonal ensemble of random matrices and QCD in three dimensions

We consider the parity-invariant Dirac operator with a mass term in three-dimensional QCD for N_c=2. We show that there exists a basis in which the matrix elements of the Euclidean Dirac operator are real. We then construct a random matrix theory with the same global symmetries as two-color QCD_3 and derive from here the finite-volume partition function for the latter in the static limit. Assuming there is spontaneous breaking of flavor and/or parity, we read off the flavor symmetry-breaking pattern that might occur in such a theory. We also derive the first Leutwyler-Smilga-like sum rule for the eigenvalues of the Dirac operator