Wigner-Dyson Statistics from the Keldysh $\sigma$-Model

The level statistics of disordered metallic grains with broken time reversal invariance is obtained from the Keldysh nonlinear $\sigma$-model. The basic strategy of the approach—a nonperturbative integration over all saddle points of the $\sigma$-model manifold—might prove useful in the analysis of problems involving disorder and interactions.