Nonperturbative results for level correlations from the replica nonlinear sigma model

We show that for all three standard symmetry classes (unitary, orthogonal, and symplectic), the conventional replica nonlinear sigma model gives the c orrect nonperturbative result for the two-level correlation functions R-2(o mega) of electrons in disordered metals in the limit of large omega. In thi s limit, nonperturbative oscillatory contributions arise from a degenerate saddle-point manifold within this sigma model that correspond to the replic a-symmetry breaking. Moreover, we demonstrate that in the unitary case the very same results can be extracted from the exact integral representation f or R-2(omega) used by Verbaarschot and Zirnbauer [J. Phys. A 17, 1093 (1985 )] to criticize the replica trick. [S0163-1829(99)01330-2].