Weak supersymmetry

Abstract

We 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 {\it interacting} theory for $d\ge 3$. 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.

14 pages LaTeX, final version to be published in Phys.Lett. B

References in corpus (2)

• Nonlinear supersymmetry in Quantum Mechanics: algebraic properties and differential representation
• Effective Lagrangians for (0+1) and (1+1) dimensionally reduced versions of D=4 N=2 SYM theory

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