$\cal N$=2 SUSY and the Hexipentisteriruncicantitruncated 7-Simplex
| Autor: | Cianciara, Aleksander J., Coleman, Zachary, Gates Jr., S. James, Lee, Youngik Tom, Zhang, Ziyang |
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| Rok vydání: | 2023 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | We study algorithms for recursively creating arbitrary N-extended `supermultiplets' given minimal matrix representations of off-shell, N = 1 supermultiplet matrices. We observe connections between the color vertex problems in graph theory and the different supermultiplet sets locations in the permutahedron by using the concepts of truncation and chromatic number. The concept of `hopping operators' is introduced, constructed, and then used to partition the 8! vertices of the permutahedron. We explicitly partition these into 5,040 octets constrained in locations on the permutahedron by a magic number rule. Boolean factors in this recursive construction are shown to obey a doubly even binary flip rule. Although these hopping operators do not generally constitute normal subgroups of the permutation group, we find that `ab-normal cosets' exist where the same left- and right-hoppers appear as unordered sets. Finally, using computer simulations, we investigate the types of faces on higher-order permutahedron which may give rise to lower-order supermultiplets. Comment: 35 pages, 12 figures |
| Databáze: | arXiv |
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