Relating Doubly-Even Error-Correcting Codes, Graphs, and Irreducible Representations of N-Extended Supersymmetry

Abstract

Previous work has shown that the classification of indecomposable off-shell representations of N-supersymmetry, depicted as Adinkras, may be factored into specifying the topologies available to Adinkras, and then the height-assignments for each topological type. The latter problem being solved by a recursive mechanism that generates all height-assignments within a topology, it remains to classify the former. Herein we show that this problem is equivalent to classifying certain (1) graphs and (2) error-correcting codes.

19 pages

References in corpus (5)

• Adinkras: A Graphical Technology for Supersymmetric Representation Theory
• A Theory of Spinning Particles for Large N-extended Supersymmetry
• When Superspace Is Not Enough
• Topology Types of Adinkras and the Corresponding Representations of N-Extended Supersymmetry
• Irreps and Off-shell Invariant Actions of the N-extended Supersymmetric Quantum Mechanics

Cited by in corpus (15)

• 4D, N = 1 Supersymmetry Genomics (I)
• Topology Types of Adinkras and the Corresponding Representations of N-Extended Supersymmetry
• Weaving Worldsheet Supermultiplets from the Worldlines Within
• From Diophantus to Supergravity and massless higher spin multiplets
• A Lorentz Covariant Holoraumy-Induced "Gadget" From Minimal Off-Shell 4D, N = 1 Supermultiplets
• 4D, N = 1 Supersymmetry Genomics (II)
• Automorphism Properties of Adinkras
• Think Different: Applying the Old Macintosh Mantra to the Computability of the SUSY Auxiliary Field Problem
• Superspace: a Comfortably Vast Algebraic Variety
• Properties of HYMNs in Examples of Four-Color, Five-Color, and Six-Color Adinkras
• Structural Theory of 2-d Adinkras
• N=4 and N=8 SUSY Quantum Mechanics and Klein's Vierergruppe
• A Computer Algorithm For Engineering Off-Shell Multiplets With Four Supercharges On The World Sheet
• Adinkras: Graphs of Clifford Algebra Representations, Supersymmetry, and Codes
• Spacetime Spin and Chirality Operators for Minimal 4D, $\mathcal{N}$ = 1 Supermultiplets From BC${}_4$ Adinkra-Tessellation of Riemann Surfaces