Two-matrix string model as constrained (2+1)-dimensional integrable system

We show that the 2-matrix string model corresponds to a coupled system of 2+1-dimensional KP and modified KP ((m)KP2+1) integrable equations subject to a specific “symmetry” constraint. The latter together with the Miura-Konopelchenko map for (m)KP2+1 are the continuum incarnation of the matrix string equation. The (m)KP2+1 Miura and Bäcklund transformations are natural consequences of the underlying lattice structure. The constrained (m)KP2+1 system is equivalent to a 1+1-dimensional generalized KP-KdV hierarchy related to graded SL(3,1). We provide an explicit representation of this hierarchy, including the associated W(2,1)-algebra of the second Hamiltonian structure, in terms of free currents.