Quantum Chiral Superfields

TL;DR

This paper constructs supersymmetric extensions of conformal and Minkowski spaces using super Grassmannians and twistor coordinates, providing a geometric framework for conformal superspace and Minkowski superspace.

Contribution

It introduces a geometric realization of supersymmetric conformal and Minkowski spaces via super Grassmannians and twistor coordinates, extending classical constructions.

Findings

Realization of supersymmetric conformal space as a super Grassmannian

Description of chiral superfields on super Grassmannians

Connection of super Grassmannians to twistor and Minkowski superspaces

Abstract

We define the ordinary Minkowski space inside the conformal space according to Penrose and Manin as homogeneous spaces for the Poincar\'e and conformal group respectively. We realize the supersymmetric (SUSY) generalizations of such homogeneous spaces over the complex and the real fields. We finally investigate chiral (antichiral) superfields, which are superfields on the super Grassmannian, Gr(2|1, 4|1), respectively on Gr(2|0, 4|1). They ultimately give the twistor coordinates necessary to describe the conformal superspace as the flag Fl(2|0, 2|1; 4|1) and the Minkowski superspace as its big cell.