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arXiv · hep-th/9407017

Two-Matrix String Model as Constrained (2+1)-Dimensional Integrable System

H. Aratyn·E. Nissimov·S. Pacheva·A. H. Zimerman
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Abstract

We show that the 2-matrix string model corresponds to a coupled system of $2+1$-dimensional KP and modified KP ($\KPm$) integrable equations subject to a specific ``symmetry'' constraint. The latter together with the Miura-Konopelchenko map for $\KPm$ are the continuum incarnation of the matrix string equation. The $\KPm$ Miura and Bäcklund transformations are natural consequences of the underlying lattice structure. The constrained $\KPm$ system is equivalent to a $1+1$-dimensional generalized KP-KdV hierarchy related to graded ${\bf SL(3,1)}$. We provide an explicit representation of this hierarchy, including the associated ${\bf W(2,1)}$-algebra of the second Hamiltonian structure, in terms of free currents.

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H. Aratyn, E. Nissimov, S. Pacheva, A. H. Zimerman. 1994-07-04. Two-Matrix String Model as Constrained (2+1)-Dimensional Integrable System. https://doi.org/10.1016/0370-2693(94)01255-5

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