Pure fermionic twistor like model & target space supersymmetry

TL;DR

This paper develops a fermionic twistor model using world line fermions in various dimensions, revealing a natural emergence of 4D  target space supersymmetry and exploring higher spin solutions.

Contribution

It introduces a pure fermionic twistor-like construction and demonstrates its connection to 4D  supersymmetry and higher spin solutions.

Findings

Quantum spectrum exhibits 4D  target space supersymmetry.

Fermi antisymmetry constraints are solved via twistor-like variables.

Higher spin solutions of the fermionic constraints are discussed.

Abstract

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.