Adinkra (In)Equivalence From Coxeter Group Representations: A Case Study
| Autor: | Tristan Hübsch, S. James Gates, Isaac Chappell |
|---|---|
| Rok vydání: | 2012 |
| Předmět: |
High Energy Physics - Theory
Physics Nuclear and High Energy Physics Coxeter group FOS: Physical sciences Astronomy and Astrophysics Mathematical Physics (math-ph) Permutation group Automorphism Atomic and Molecular Physics and Optics Group representation Algebra Permutation High Energy Physics - Theory (hep-th) Hodge dual Equivalence (measure theory) Mathematical Physics Supersymmetry algebra |
| DOI: | 10.48550/arxiv.1210.0478 |
| Popis: | Using a Mathematica code, we present a straightforward numerical analysis of the 384-dimensional solution space of signed permutation 4x4 matrices, which in sets of four provide representations of the GR(4,4) algebra, closely related to the N=1 (simple) supersymmetry algebra in 4-dimensional spacetime. 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 GR(4,4) representations into three suggestive classes. Comment: 23 pages, 6 figures (v.2: numerical data corrections in appendix C) |
| Databáze: | OpenAIRE |
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