Weak supersymmetry

Details Weak supersymmetry Weak supersymmetry

2003-11-04

arxiv.org/abs/hep-th/0311023v2

Phys.Lett.B585:173-179,2004

Physics

High Energy Physics

High Energy Physics - Theory

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

Scientific paper

10.1016/j.physletb.2004.01.070

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 $d \geq 3$. 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.

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