N = 2 local and N = 4 non-local reductions of supersymmetric KP hierarchy in N = 2 superspace Original Research Article

An N = 4 supersymmetric matrix KP hierarchy is proposed and a wide class of its reductions which are characterized by a finite number of fields are described. This class includes the one-dimensional reduction of the two-dimensional N = (2⋎2) superconformal Toda lattice hierarchy possessing the N = 4 supersymmetry — the N = 4 Toda chain hierarchy - which may be relevant in the construction of supersymmetric matrix models. The Lax-pair representations of the bosonic and fermionic flows, corresponding local and non-local Hamiltonians, finite and infinite discrete symmetries, the first two Hamiltonian structures and the recursion operator connecting all evolution equations and the Hamiltonian structures of the N = 4 Toda chain hierarchy are constructed in explicit form. Is secondary reduction to the N = 4 supersymmetric α = − 2 KdV hierarchy is