**7. Outlook: Graphene and supersymmetry**

Fundamental interactions are rather successful formulated in terms of Yang-Mills theories with large gauge groups, stipulating that symmetry breaking is occurring in the ground state. The idea of supersymmetry or supergravity, anticipated to some extent already by Hermann Weyl [42], goes in the same direction but so far lacks empirical support in particle physics.

Recently, graphene [33] as a new material has attracted a lot of attention because its charge carriers can be described by massless Dirac fields, cf. Ref. [41], whereas the flexural models of the 2D membrane of graphene have been tentatively considered as membranes, cf. Ref. [25], evolving in 2 + 1 dimensional curved, but conformally flat spacetime [24]. There are also indications of dislocations [9] related to torsion.

A related topological framework with a coupling to Dirac fields in 3D has been considered before by Lemke and Mielke [27]. It seems to be feasible to enlarge the dynamical framework of the theory by including supersymmetry, cf. Ref. [17] and apply the topological ideas developed to some extent in this paper.
