  We construct a supersymmetric model of interacting Majorana fermions on the
kagome lattice. In the infinite-coupling limit, the model exhibits an
extensively degenerate ground state manifold separated in two topological
sectors, in addition to two parity supersectors. An exact solution for
thin-torus geometries allows us to analytically construct the entire
zero-energy ground state manifold. Upon inclusion of hopping terms with energy
scale $g$, the supersymmetry is spontaneously broken with the ground state
energy density scaling as $g^4$. We also briefly discuss the non-interacting
limit of the model, which exhibits a zero-energy flat band and Majorana Chern
bands.
