Adinkras for Clifford Algebras, and Worldline Supermultiplets

Abstract

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.

arXiv comment54 pages, 8 tables with many illustrations

References in corpus (8)

• Adinkras: A Graphical Technology for Supersymmetric Representation Theory
• A Theory of Spinning Particles for Large N-extended Supersymmetry
• Towards Mirror Symmetry as Duality for Two-Dimensional Abelian Gauge Theories
• Ultra-Multiplets: A New Representation of Rigid 2D, N = 8 Supersymmetry
• When Superspace Is Not Enough
• Topology Types of Adinkras and the Corresponding Representations of N-Extended Supersymmetry
• Vector Multiplets and the Phases of N = 2 Theories in 2D Through the Looking Glass
• Adinkras and the Dynamics of Superspace Prepotentials

Cited by in corpus (6)

• Weaving Worldsheet Supermultiplets from the Worldlines Within
• Pure and entangled N=4 linear supermultiplets and their one-dimensional sigma-models
• On General Off-Shell Representations of Worldline (1D) Supersymmetry
• On Supermultiplet Twisting and Spin-Statistics
• Creating Infinitesimal Generators And Robust Messages With Adinkras
• Adinkras: Graphs of Clifford Algebra Representations, Supersymmetry, and Codes