Quantum supertwistors

TL;DR

This paper constructs an explicit star product on super Minkowski space using supertwistor formalism and quantum deformation of superconformal groups, providing a concrete example of noncommutative superspace geometry.

Contribution

It introduces an explicit super star product on Minkowski superspace via supertwistor formalism and quantum group techniques, linking supergeometry with noncommutative geometry.

Findings

Explicit super star product expression derived

Quantization achieved through quantum deformations of supergroups

Calculations performed in Manin's formalism

Abstract

In this paper we give an explicit expression for a star product on the super Minkowski space written in the supertwistor formalism. The big cell of the super Grassmannian Gr(2|0, 4|1) is identified with the chiral, super Minkowki space. The super Grassmannian is an homogeneous space under the action of the complexification SL(4|1) of SU(2,2|1), the superconformal group in dimension 4, signature (1,3) and supersymmetry N=1. The quantization is done by substituting the groups and homogeneous spaces by their quantum deformed counterparts. The calculations are done in Manin's formalism. When we restrict to the big cell we can compute explicitly an expression for the super star product in the Minkowski superspace associated to this deformation and the choice of a certain basis of monomials.