Adinkras for Clifford Algebras, and Worldline Supermultiplets

Details Adinkras for Clifford Algebras, and Worldline Supermultiplets Adinkras for Clifford Algebras, and Worldline Supermultiplets

2008-11-20

arxiv.org/abs/0811.3410v1

Physics

High Energy Physics

High Energy Physics - Theory

54 pages, 8 tables with many illustrations

Scientific paper

Adinkras are a graphical depiction of representations of the N-extended supersymmetry algebra in one dimension, on the worldline. These diagrams represent the component fields in a supermultiplet as vertices, and the action of the supersymmetry generators as edges. In a previous work, we showed that the chromotopology (topology with colors) of an Adinkra must come from a doubly even binary linear code. Herein, we relate Adinkras to Clifford algebras, and use this to construct, for every such code, a supermultiplet corresponding to that code. In this way, we correlate the well-known classification of representations of Clifford algebras to the classification of Adinkra chromotopologies.

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