  Rudnick recently proved that the spectral number variance for the Laplacian
of a large compact hyperbolic surface converges, in a certain scaling limit and
when averaged with respect to the Weil-Petersson measure on moduli space, to
the number variance of the Gaussian Orthogonal Ensemble of random matrix
theory. In this note we extend Rudnick's approach to show convergence to the
Gaussian Unitary Ensemble for twisted Laplacians which break time-reversal
symmetry, and to the Gaussian Symplectic Ensemble for Dirac operators. This
addresses a question of Naud, who obtained analogous results for twisted
Laplacians on high genus random covers of a fixed compact surface.
