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 | |
| 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.