Superfield representations of superconformal groups

TL;DR

This paper constructs superconformal group representations as fields on various superspaces, showing how all N=4 superconformal representations can be obtained from Maxwell multiplets on analytic superspace, and relates this to oscillator methods.

Contribution

It introduces a unified superfield framework for superconformal representations across different superspaces and connects it with oscillator constructions.

Findings

All N=4 superconformal representations can be derived from Maxwell multiplets on analytic superspace.

Unconstrained superfields on analytic superspace can represent any unitary irreducible superconformal representation.

A natural correspondence between oscillator and superfield constructions is established.

Abstract

Representations of four dimensional superconformal groups are constructed as fields on many different superspaces, including super Minkowski space, chiral superspace, harmonic superspace and analytic superspace. Any unitary irreducible representation can be given as a field on any one of these spaces if we include fields which transform under supergroups. In particular, on analytic superspaces, the fields are unconstrained. One can obtain all representations of the N=4 complex superconformal group $PSL(4|4)$ with integer dilation weight from copies of the Maxwell multiplet on $(4,2,2)$ analytic superspace. This construction is compared with the oscillator construction and it is shown that there is a natural correspondence between the oscillator construction of superconformal representations and those carried by superfields on analytic superspace.