Superfield equations in the Berezin-Kostant-Leites category

TL;DR

This paper demonstrates how superfield equations in the Berezin-Kostant-Leites framework can be used to realize specific unitary representations of the super Poincaré group in four dimensions, connecting supersymmetric equations with representation theory.

Contribution

It introduces a supersymmetric extension of the Fourier transform and proves that superfield equations realize irreducible unitary representations with positive mass and zero superspin.

Findings

Superfield equations can be represented by supersymmetric equations in the Berezin-Kostant-Leites sense.

A supersymmetric Fourier transform extension is constructed.

These equations realize specific irreducible unitary representations of the super Poincaré group.

Abstract

Using the functor of points, we prove that the Wess-Zumino equations for massive chiral superfields in dimension 4|4 can be represented by supersymmetric equations in terms of superfunctions in the Berezin-Kostant-Leites sense (involving ordinary fields, with real and complex valued components). Then, after introducing an appropriate supersymmetric extension of the Fourier transform, we prove explicitly that these supersymmetric equations provide a realization of the irreducible unitary representations with positive mass and zero superspin of the super Poincar\'e group in dimension 4|4.