Higher supergeometry for the super-σ-model

The article presents a status report and reviews a programme of a systematic (super)algebraisation and geometrisation of the canonical data (vacua, symme-tries, dualities, defectsetc.) of super-σ-models for super-p-branes of superstringtheory and M-theory on homogeneous spaces of supersymmetry Lie supergroups and of a κ-symmetry-equivariant geometrisation of the classes in the corresponding Cartan–Eilenberg cohomology. The programme draws upon and generalises essentially the much successful higher-geometric and -algebraic approach to the two-dimensional non-linear bosonic σ-model of string theory.