Fractional Supersymmetry As a Matrix Model

Details Fractional Supersymmetry As a Matrix Model Fractional Supersymmetry As a Matrix Model

2001-01-25

arxiv.org/abs/hep-th/0101172v1

Class.Quant.Grav. 16 (1999) 1793-1804

Physics

High Energy Physics

High Energy Physics - Theory

Latex,no figure,17pages

Scientific paper

10.1088/0264-9381/16/6/313

Using parafermionic field theoretical methods, the fundamentals of 2d fractional supersymmetry ${\bf Q}^{K} =P$ are set up. Known difficulties induced by methods based on the $U_{q}(sl(2))$ quantum group representations and non commutative geometry are overpassed in the parafermionic approach. Moreover we find that fractional supersymmetric algebras are naturally realized as matrix models. The K=3 case is studied in details. Links between 2d $({1\over 3},0)$ and $(({1\over 3}^{2}),0)$ fractional supersymmetries and N=2 U(1) and N=4 su(2) standard supersymmetries respectively are exhibited. Field theoretical models describing the self couplings of the matter multiplets $(0^{2},({1\over 3})^{2},({2\over 3})^{2})$ and $(0^{4},({1\over 3})^{4},({2\over 3})^{4})$ are given.

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