Adinkras for Clifford Algebras, and Worldline Supermultiplets

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. PACS: 04.65.+e ar X iv :0 81 1. 34 10 v1 [ he pth ] 2 0 N ov 2 00 8