New results in supersymmetric quantum mechanics
Francesco Toppan
CBPF, Rio de Janeiro, Brazil
The classification of linear finite multiplets of irreducible representations of the N-extended 1D supersymmetry algebra, for arbitrary N, is presented for the first time. Classes of off-shell invariants for arbitrary N, obtained in terms of BRST cohomology, are constructed. On-shell actions invariant under non-linear supersymmetry are constructed in terms of multilinearly constrained multiplets. Our approach, based on the irreducible representations, does not require the introduction of superfields (which are not available for N>= 8). Supersymmetric quantum mechanical models, susy sigma models, etc. are systematically constructed, overcoming the N=8 barrier. We remind that the dimensional reduction of the maximal sugra/M-theory will lead to an N=32 1D supersymmetric quantum mechanical model, while applications of supersymmetry in condensed matter phenomena often require N-> infty.