Supersymmetry without hermiticity
  A new model of supersymmetry between bosons and fermions is proposed. Its representation space is spanned by states with PT symmetry and real energies but the inter-related partner Hamiltonians themselves remain complex and non-Hermitian. The formalism admits vanishing Witten index. 
M. Znojil, F. Cannata, B. Bagchi and R. Roychoudhury