On Harmonic Superspaces and Superconformal Fields in Four Dimensions

TL;DR

This paper explores the structure of superconformal representations in four dimensions using harmonic superspaces, revealing new ways to describe short multiplets and their transformations explicitly.

Contribution

It introduces a novel approach to constructing and analyzing short superconformal multiplets via harmonic superspaces and parabolic induction.

Findings

Short representations can be obtained by parabolic induction.

Multiple descriptions of the same multiplet as superfields are possible.

Explicit superconformal transformation formulas are provided.

Abstract

Representations of four-dimensional superconformal groups on harmonic superfields are discussed. It is shown how various short representations can be obtained by parabolic induction. It is also shown that such short multiplets may admit several descriptions as superfields on different superspaces. In particular, this is the case for on-shell massless superfields. This allows a description of short representations as explicit products of fundamental fields. Superconformal transformations of analytic fields in real harmonic superspaces are given explicitly.