The Green–Schwarz superstring as an asymmetric model of a chiral field

A new class of two-dimensional $\sigma$-models of the Wess–Zumino type is constructed. The target manifold of these models is coset space $G\otimes G/G^-$ where supergroup $G$ is obtained by contraction from an arbitrary semi-simple Lie supergroup and $G^-$ is some abelian subgroup of translations in $G\otimes G$. It is shown that the equations of motion following from the Wess–Zumino type action of these model admit a zero-curvature representation.