Pure fermionic twistor like model & target space supersymmetry

Details Pure fermionic twistor like model & target space supersymmetry Pure fermionic twistor like model & target space supersymmetry

2006-05-17

arxiv.org/abs/hep-th/0605167v1

Physics

High Energy Physics

High Energy Physics - Theory

Scientific paper

Using world line fermions $\Upsilon_{\pm}^{m}=\Upsilon_{\pm}^{m}(\tau) $ valued in vector representation of $SO(d,4-d) $ with $d=2,3,4,$ we develop a pure fermionic analog of Penrose twistor construction. First, we show that Fermi antisymmetry requiring $(\Upsilon_{\pm}^{m}) ^{2}=0$ can be solved by using twistor like variables. Then we study the corresponding dual twistor like field action and show that quantum spectrum exhibits naturally 4D $\mathcal{N}=1$ target space supersymmetry. Higher spin world line field solutions of the constraint $(\Pi_{s}^{m}) ^{2}=0$, $s\in \mathbb{Z}$ are also discussed.

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