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

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 $\mathbf{SL}(3,1)$. We provide an explicit representation of this hierarchy, including the associated $\mathbf{W}(2,1)$-algebra of the second Hamiltonian structure, in terms of free currents.

12+1 pgs., LaTeX, preprint: BGU-94 / 15 / June-PH, UICHEP-TH/94-6

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Cited by in corpus (4)

• Darboux-Backlund Solutions of SL(p,q) KP-KdV Hierarchies, Constrained Generalized Toda Lattices, and Two-Matrix String Model
• Affine Lie Algebraic Origin of Constrained KP Hierarchies
• Hungry Volterra equation, multi boson KP hierarchy and Two Matrix Models
• Exact Correlators of Two-Matrix Models