Nonperturbative results for level correlations from the replica nonlinearσmodel

We show that for all three standard symmetry classes (unitary, orthogonal, and symplectic), the conventional replica nonlinear σ model gives the correct nonperturbative result for the two-level correlation functions R₂(ω) of electrons in disordered metals in the limit of large ω. In this limit, nonperturbative oscillatory contributions arise from a degenerate saddle-point manifold within this σ model that correspond to the replica-symmetry breaking. Moreover, we demonstrate that in the unitary case the very same results can be extracted from the exact integral representation for R₂(ω) used by Verbaarschot and Zirnbauer [J. Phys. A 17, 1093 (1985)] to criticize the replica trick.