A Cartan tale of the orbifold superstring

A geometrisation scheme internal to the category of Lie supergroups is discussed for the supersymmetric de Rham cocycles on the super-Minkowski group $\,\mathbb{T}\,$ which determine the standard super-$p$-brane dynamics with that target, and interpreted within Cartan's approach to the modelling of orbispaces of group actions by homotopy quotients. The ensuing higher geometric objects are shown to carry a canonical equivariant structure for the action of a discrete subgroup of $\,\mathbb{T}$, which results in their descent to the corresponding orbifolds of $\,\mathbb{T}\,$ and in the emergence of a novel class of superfield theories with defects.