A Counter-Example to a Putative Classification of 1-Dimensional, N-extended Supermultiplets

TL;DR

This paper provides a counter-example challenging a recent claim that classifies 1-dimensional, N-extended supermultiplets solely based on component field counts across all dimensions.

Contribution

It introduces a specific counter-example that disproves the uniqueness of the classification scheme for these supermultiplets.

Findings

Counter-example invalidates the previous classification claim

Shows that component field counts do not uniquely determine supermultiplet types

Highlights the need for additional criteria in classifying supermultiplets

Abstract

We present a counter-example to the recent claim that supermultiplets of N-extended supersymmetry with no central charge and in 1-dimension are specified unambiguously by providing the numbers of component fields in all available engineering dimensions within the supermultiplet.