supersymmetric Toda lattice hierarchy in N = ( 2 | 2 ) superspace

An N=(2|2) superfield formulation of the N=(2|2) supersymmetric Toda lattice hierarchy is proposed, and its five real forms are presented. 1. Introduction. Recently the N=(1|1) supersymmetric generalization of the Darboux transformation was proposed in [1], and an infinite class of bosonic and fermionic solutions of its symmetry equation was constructed in [1, 2]. These solutions generate bosonic and fermionic flows of the N=(1|1) supersymmetric Toda lattice hierarchy in the same way as their bosonic counterparts – the solutions of the symmetry equation of the Darboux transformation [3] – produce the flows of the bosonic Toda lattice hierarchy. Actually, the N=(1|1) Toda lattice hierarchy is N=(2|2) supersymmetric, and henceforth we shall call it the N=(2|2) Toda lattice hierarchy. Naturally, the quest for its N=(2|2) superfield formulation arises.