Pure fermionic twistor like model & target space supersymmetry

Abstract

Using world line fermions ${{\rm Y}}_{\pm }^m={{\rm Y}}_{\pm }^m(\tau )$ 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 $({{\rm Y}}_{\pm }^m{)}^2=0$ 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.