2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/112524Using world line fermions $Υ_{\pm}^{m}=Υ_{\pm}^{m}(τ) $ 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 $(Υ_{\pm}^{m}) ^{2}=0$ 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 $(Π_{s}^{m}) ^{2}=0$, $s\in \mathbb{Z}$ are also discussed.High Energy Physics - Theorytext