4D $$ \mathcal{N} $$ = 1 Kaluza-Klein superspace

Motivated by recent efforts to encode 11D supergravity in 4D $$ \mathcal{N} $$ N = 1 superfields, we introduce a general covariant framework relevant for describing any higher dimensional supergravity theory in external 4D $$ \mathcal{N} $$ N = 1 superspace with n additional internal coordinates. The superspace geometry admits both external and internal diffeomorphisms and provides the superfields necessary to encode the components of the higher dimensional vielbein, except for the purely internal sector, in a universal way that depends only on the internal dimension n. In contrast, the $$ \mathcal{N} $$ N = 1 superfield content of the internal sector of the metric is expected to be highly case dependent and involve covariant matter superfields, with additional hidden higher dimensional Lorentz and supersymmetry transformations realized in a non-linear manner.