Multi-matrix models without continuum limit

Details Multi-matrix models without continuum limit Multi-matrix models without continuum limit

1992-12-10

arxiv.org/abs/hep-th/9212070v2

Nucl.Phys. B405 (1993) 191-227

Physics

High Energy Physics

High Energy Physics - Theory

31 pages, LateX, SISSA-ISAS 211/92/EP

Scientific paper

We derive the discrete linear systems associated to multi--matrix models, the corresponding discrete hierarchies and the appropriate coupling conditions. We also obtain the $W_{1+\infty}$ constraints on the partition function. We then apply to multi--matrix models the technique, developed in previous papers, of extracting hierarchies of differential equations from lattice ones without passing through a continuum limit. In a q--matrix model we find 2q coupled differential systems. The corresponding differential hierarchies are particular versions of the KP hierarchy. We show that the multi--matrix partition function is a $\tau$--function of these hierarchies. We discuss a few examples in the dispersionless limit.

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