Superconformal Selfdual Sigma-Models

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 $\mathfrak{G}\mathrm{/}\mathfrak{H}$ 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 $\text{tfG}\mathrm{/}\text{tfH}$ models constrained by a selfduality equation, with $\text{tfG}$ the loop extension of $\mathfrak{G}$ and $\text{tfH}$ a maximal subgroup. It ensures that these models have a hidden global $\text{tfG}$ symmetry together with a local $\text{tfH}$ gauge symmetry.