A Letter Highlighting Matrix Mapping in Minimal 4D, ${\mathbf {\cal N}}$ = 1 On-Shell Supermultiplet Representations

TL;DR

This paper investigates the structure of 4D, ${ m f }$=1 supermultiplets, revealing that the double tensor supermultiplet has a fundamentally different eigenvalue profile, indicating challenges in embedding it into off-shell frameworks.

Contribution

It introduces a matrix mapping approach based on eigenvalues to analyze supermultiplet representations, highlighting the unique nature of the double tensor supermultiplet.

Findings

Eigenvalues distinguish supermultiplet types.

Double tensor supermultiplet is fundamentally different.

Embedding into off-shell structures is likely problematic.

Abstract

On the basis of comparing eigenvalues of an operator ${\hat {\mathbf{\cal C}}}{}^{({\cal R})}$, that proved useful in distinguishing how off-shell 4D, $\cal N$ = 1 supermultiplets become off-shell 4D, $\cal N$ = 2 supermultiplets, the double tensor supermultiplet is shown to be radically different for other known multiplets. This suggests difficulties, if not impossibilities, to embed it into an off-shell structure.