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Exact solvability is claimed for nonlinear replica sigma models derived inthe context of random matrix theories. Contrary to other approaches reported inthe literature, the framework outlined does not rely on traditional "replicasymmetry breaking" but rests on a previously unnoticed exact relation betweenreplica partition functions and Painleve transcendents. While expected to beapplicable to matrix models of arbitrary symmetries, the method is used totreat fermionic replicas for the Gaussian unitary ensemble (GUE), chiral GUE(symmetry classes A and AIII in Cartan classification) and Ginibre's ensembleof complex non-Hermitean random matrices. Further applications are brieflydiscussed.Comment: published version, 4 pages, revtex

Replica Field Theories, Painlevé Transcendents, and Exact Correlation Functions