Replica Limit of the Toda Lattice Equation

K. Splittorff; J. J.M. Verbaarschot

doi:10.1103/PhysRevLett.90.041601

Replica Limit of the Toda Lattice Equation

K. Splittorff
, J. J.M. Verbaarschot

Physics and Astronomy

Stony Brook University

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

In a recent breakthrough Kanzieper showed that it is possible to obtain exact nonperturbative random matrix results from the replica limit of the corresponding Painlevé equation. In this article we analyze the replica limit of the Toda lattice equation and obtain exact expressions for the two-point function of the Gaussian unitary ensemble and the resolvent of the chiral unitary ensemble. In the latter case both the fully quenched and the partially quenched limit are considered. This derivation explains in a natural way the appearance of both compact and noncompact integrals, the hallmark of the supersymmetric method, in the replica limit of the expression for the resolvent.

Original language	English
Pages (from-to)	4
Number of pages	1
Journal	Physical Review Letters
Volume	90
Issue number	4
DOIs	https://doi.org/10.1103/PhysRevLett.90.041601
State	Published - 2003

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10.1103/PhysRevLett.90.041601

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Replica Limit of the Toda Lattice Equation

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