Scaling Self-Similar Formulation of the String Equations of the Hermitian Matrix Model

Details Scaling Self-Similar Formulation of the String Equations of the Hermitian Matrix Model Scaling Self-Similar Formulation of the String Equations of the Hermitian Matrix Model

1993-07-04

arxiv.org/abs/hep-th/9307020v2

Phys.Lett. B317 (1993) 341-345

Physics

High Energy Physics

High Energy Physics - Theory

12 pages in AMS-LaTeX, AMS-LaTeXable version

Scientific paper

10.1016/0370-2693(93)91005-8

The string equation appearing in the double scaling limit of the Hermitian one--matrix model, which corresponds to a Galilean self--similar condition for the KdV hierarchy, is reformulated as a scaling self--similar condition for the Ur--KdV hierarchy. A non--scaling limit analysis of the one--matrix model has led to the complexified NLS hierarchy and a string equation. We show that this corresponds to the Galilean self--similarity condition for the AKNS hierarchy and also its equivalence to a scaling self--similar condition for the Heisenberg ferromagnet hierarchy.

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