Abstract
The local Sugawara constructions of the "small" N=4 SCA in terms of supercurrents of N=2 extensions of the affine [Formula: see text] and [Formula: see text] algebras are investigated. The associated super mKdV type hierarchies induced by N=4 SKdV ones are defined. In the [Formula: see text] case the existence of two nonequivalent Sugawara constructions is found. The "long" one involves all the affine [Formula: see text] currents, while the "short" one deals only with those from the subalgebra [Formula: see text]. As a consequence, the [Formula: see text]-valued affine superfields carry two nonequivalent mKdV type super-hierarchies induced by the correspondence between "small" N=4 SCA and N=4 SKdV hierarchy. However, only the first hierarchy possesses genuine global N=4 supersymmetry. We discuss peculiarities of the realization of this N=4 supersymmetry on the affine supercurrents.
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