Title

Adinkra (In)Equivalence From Coxeter Group Representations:

Keywords

Off-shell supermultiplets; Quantum mechanics; Supersymmetry

Abstract

Using a MathematicaTM code, we present a straightforward numerical analysis of the 384-dimensional solution space of signed permutation 4×4 matrices, which in sets of four, provide representations of the (4, 4) algebra, closely related to the = 1 (simple) supersymmetry algebra in four-dimensional space-time. Following after ideas discussed in previous papers about automorphisms and classification of adinkras and corresponding supermultiplets, we make a new and alternative proposal to use equivalence classes of the (unsigned) permutation group S4 to define distinct representations of higher-dimensional spin bundles within the context of adinkras. For this purpose, the definition of a dual operator akin to the well-known Hodge star is found to partition the space of these (4, 4) representations into three suggestive classes. © World Scientific Publishing Company.

Publication Date

3-10-2014

Publication Title

International Journal of Modern Physics A

Volume

29

Issue

6

Number of Pages

-

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1142/S0217751X14500298

Socpus ID

84897801417 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/84897801417

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