Decomposition and Oxidation of the N-Extended Supersymmetric Quantum Mechanics Multiplets

TL;DR

This paper provides an algebraic classification of the connectivities of supermultiplets in N-extended supersymmetric quantum mechanics, revealing their decomposition structures and introducing diagrams that link different supermultiplets.

Contribution

It introduces a novel algebraic framework for understanding the inequivalent connectivities and decompositions of supermultiplets up to N=10 in supersymmetric quantum mechanics.

Findings

Classified inequivalent connectivities for N≤10 supermultiplets.

Proved that connectivities for N=5 and N=9 arise from specific decompositions.

Presented 'Oxido-reduction' diagrams linking supermultiplets across different N.

Abstract

We furnish an algebraic understanding of the inequivalent connectivities (computed up to $N\leq 10$) of the graphs associated to the irreducible supermultiplets of the N-extended Supersymmetric Quantum Mechanics. We prove that the inequivalent connectivities of the N=5 and N=9 irreducible supermultiplets are due to inequivalent decompositions into two sets of N=4 (respectively, N=8) supermultiplets. "Oxido-reduction" diagrams linking the irreducible supermultiplets of the N=5,6,7,8 supersymmetries are presented. We briefly discuss these results and their possible applications.