A range of bosonic models can be expressed as (sometimes generalized) $\sigma$-models, with equations of motion coming from a selfduality constraint. We show that in D=2, this is easily extended to supersymmetric cases, in a superspace approach. In particular, we find that the configurations of fields of a superconformal $\mathfrak{ G}/\mathfrak{ H}$ coset models which satisfy some selfduality constraint are automatically solutions to the equations of motion of the model. Finally, we show that symmetric space $\sigma$-models can be seen as infinite-dimensional $\tfG/\tfH$ models constrained by a selfduality equation, with $\tfG$ the loop extension of $\mathfrak{ G}$ and $\tfH$ a maximal subgroup. It ensures that these models have a hidden global $\tfG$ symmetry together with a local $\tfH$ gauge symmetry.
Categories: hep-th