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

Abstract

We furnish an algebraic understanding of the inequivalent connectivities (computed up to N ≤ 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.

On nonminimal ${\cal N}=4$N=4 supermultiplets in 1D and their associated σ-models

“…Combining these results with the results presented in [10] we get that all non-minimal length-3 representations are oxidized to the maximal number N max = 8 of extended supersymmetries.…”

“…* This Section employs the techniques introduced in [10]. The presented results answer the following question: which minimal N = 5 supermultiplets can be obtained by adding an extra supersymmetry operator to a given non-minimal N = 4 supermultiplet in such a way to guarantee an overall N = 5 (1) superalgebra.…”

“…The linear representations are characterized by a series of properties which, for sake of consistency, are reviewed in Appendix A. They include the grading of the fields (in physical terms, their mass-dimension), the length and the field content of the supermultiplets [2,4], the dressing transformations [14,15,2], the association with graphs [3,5,6,9,10,11], the connectivity symbol [9,10] characterizing inequivalent representation with a given field content (the notion of inequivalent representations has been discussed in [5,6]), the mirror duality [8], etc.…”

“…We employ the techniques introduced in [9,10] and discussed in detail in those works. Therefore, here we limit ourselves to present the main results.…”

Adinkras, 0-branes, holoraumy and the SUSY QFT/QM correspondence

“…The former approach obviously will contain remnants of information about the symmetries of the higher dimensional spacetime. How are these data "downloaded" onto the theories constructed from a purely adinkra network-based [1,2,3,4,5,6,7,8,9,10] approach?…”