Multi-field representations of KP hierarchies and multi-matrix models

Details Multi-field representations of KP hierarchies and multi-matrix models Multi-field representations of KP hierarchies and multi-matrix models

1993-05-03

arxiv.org/abs/hep-th/9305005v2

Phys.Lett. B317 (1993) 329-340

Physics

High Energy Physics

High Energy Physics - Theory

14 pages, LaTeX, SISSA 53/93/EP, ASITP 93-25

Scientific paper

10.1016/0370-2693(93)91004-7

We discuss the integrable hierarchies that appear in multi--matrix models. They can be envisaged as multi--field representations of the KP hierarchy. We then study the possible reductions of this systems via the Dirac reduction method by suppressing successively one by one part of the fields. We find in this way new integrable hierarchies, of which we are able to write the Lax pair representations by means of suitable Drinfeld--Sokolov linear systems. At the bottom of each reduction procedure we find an $N$--th KdV hierarchy. We discuss in detail the case which leads to the KdV hierarchy and to the Boussinesque hierarchy, as well as the general case in the dispersionless limit.

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