Weak supersymmetry

AbstractWe explore “weak” supersymmetric systems whose algebra involves, besides Poincare generators, extra bosonic generators not commuting with supercharges. This allows one to have inequal number of bosonic and fermionic 1-particle states in the spectrum. Coleman–Mandula and Haag–Lopuszanski–Sohnius theorems forbid the presence of such extra bosonic charges in interacting theory for d⩾3. However, these theorems do not apply in one or two dimensions. For d=1, we construct a nontrivial interacting system characterized by weak supersymmetric algebra. It is related to “n-fold” supersymmetric systems and to quasi-exactly solvable systems studied earlier