Geometrical Construction of Supertwistor Theory

TL;DR

This paper develops a geometrical supertwistor theory based on the SUSY Hopf map, introducing a new incidence relation, and demonstrates its applications to massless particles and connections to superspin and SUSY quantum Hall effects.

Contribution

It presents a novel geometrical construction of supertwistor theory that naturally incorporates even SUSY and spin without complexification of Minkowski space.

Findings

Derived a new incidence relation for supertwistor theory.

Reproduced physical content of supertwistor theory through quantization.

Linked supertwistor theory to superspin formalism and SUSY quantum Hall effect.

Abstract

Supertwistor theory is geometrically constructed based on the SUSY Hopf map. We derive a new incidence relation for the geometrical supertwistor theory. The present supertwistor exhibits remarkable properties: Minkowski space need not be complexified to introduce spin degrees of freedom, and even number SUSY is {automatically} incorporated by the geometrical set-up. We also develop a theory for massless free particle in Minkowski superspace, which physically corresponds to the geometrical supertwistor theory. The spin degrees of freedom are originated from fermionic momenta as well as fermionic coordinates. The geometrical supertwistor is quantized to reproduce same physical contents as in the original supertwistor theory. Relationships to superspin formalism and SUSY quantum Hall effect are also discussed.