Harmonic Superspaces and Superconformal Fields

TL;DR

This paper explores how superconformal group representations can be realized as superfields on harmonic superflag manifolds, simplifying the description of short representations and their construction from fundamental fields.

Contribution

It introduces a unified framework for representing superconformal groups on harmonic superflag manifolds, enabling constraint-free descriptions of analytic superspaces and explicit construction of short representations.

Findings

Representations can be realized on various superflag manifolds.

Analytic superspaces do not require constraints.

Short representations can be constructed as products of fundamental fields.

Abstract

Representations of four-dimensional superconformal groups on harmonic superfields are discussed. It is argued that any representation can be given as a superfield on many superflag manifolds. Representations on analytic superspaces do not require constraints. We discuss short representations and how to obtain them as explicit products of fundamental fields. We also discuss superfields that transform under supergroups.