title: Integrability of zero-dimensional replica field theories at β=1.
abstract: Building on insights from the theory of integrable lattices, the integrability is claimed for nonlinear replica σ models derived in the context of real symmetric random matrices. Specifically, the fermionic and the bosonic replica partition functions are proven to form a single (supersymmetric) Pfaff-KP hierarchy whose replica limit is shown to reproduce the celebrated nonperturbative formula for the density-density eigenvalue correlation function in the infinite-dimensional Gaussian orthogonal ensemble. Implications of the formalism outlined are briefly discussed.
authors.affiliation: Department of Applied Mathematics, H.I.T.-Holon Institute of Technology, Holon 5810201, Israel and Fakultät für Physik, Universität Bielefeld, Bielefeld 33615, Germany.
authors.forename: Pedro
authors.initials: P
authors.lastname: Vidal
authors.forename: Eugene
authors.initials: E
authors.lastname: Kanzieper