Multi-matrix model and 2D Toda multi-component hierarchy

Changrim Ahn; Kazuyasu Shigemoto

doi:10.1016/0370-2693(91)91705-Z

Multi-matrix model and 2D Toda multi-component hierarchy

Changrim Ahn, Kazuyasu Shigemoto

Department of Physics

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10 Scopus citations

Abstract

We study the integrability of the hermitian matrix-chain model at finite N. The integrable system, constructed from the matrix integrals using orthogonal polynomials is identified with the two-dimensional Toda system with multi-component hierarchy. We derive the Lax equations, the zero curvature conditions and an infinite number of conserved quantities for this 2D Toda hierarchy. The partition function of the matrix model is proved to be the "tau-function" of this Toda system. Also, using our formalism, we derive the Virasoro constraints on the partition function of the multi-matrix model for the first time.

Original language	English
Pages (from-to)	44-50
Number of pages	7
Journal	Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics
Volume	263
Issue number	1
DOIs	https://doi.org/10.1016/0370-2693(91)91705-Z
State	Published - 4 Jul 1991

Bibliographical note

Funding Information:
We thank the SLAC library for sending us a copy of ref. \[7 \]. One of us (K.S.) thanks the members of the theory group at the Newman Laboratory at Cornell University. This work was supported in part by the National Science Foundation.

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abstract = "We study the integrability of the hermitian matrix-chain model at finite N. The integrable system, constructed from the matrix integrals using orthogonal polynomials is identified with the two-dimensional Toda system with multi-component hierarchy. We derive the Lax equations, the zero curvature conditions and an infinite number of conserved quantities for this 2D Toda hierarchy. The partition function of the matrix model is proved to be the {"}tau-function{"} of this Toda system. Also, using our formalism, we derive the Virasoro constraints on the partition function of the multi-matrix model for the first time.",

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Multi-matrix model and 2D Toda multi-component hierarchy

Abstract

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