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Integrability of zero-dimensional replica field theories at β=1
Pedro Vidal1, Eugene Kanzieper
1Department of Applied Mathematics, H.I.T.-Holon Institute of Technology, Holon 5810201, Israel and Fakultät für Physik, Universität Bielefeld, Bielefeld 33615, Germany.
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.
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