Topology Types of Adinkras and the Corresponding Representations of N-Extended Supersymmetry

Abstract

We present further progress toward a complete classification scheme for describing supermultiplets of N-extended worldline supersymmetry, which relies on graph-theoretic topological invariants. In particular, we demonstrate a relationship between Adinkra diagrams and quotients of N-dimensional cubes, where the quotient groups are subgroups of $(Z_2{)}^N$. We explain how these quotient groups correspond precisely to doubly even binary linear error-correcting codes, so that the classification of such codes provides a means for describing equivalence classes of Adinkras and therefore supermultiplets. Using results from coding theory we exhibit the enumeration of these equivalence classes for all cases up to 26 supercharges, as well as the maximal codes, corresponding to minimal supermultiplets, for up to 32 supercharges.

41 pages

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Cited by in corpus (19)

• 4D, N = 1 Supersymmetry Genomics (I)
• Relating Doubly-Even Error-Correcting Codes, Graphs, and Irreducible Representations of N-Extended Supersymmetry
• Weaving Worldsheet Supermultiplets from the Worldlines Within
• From Diophantus to Supergravity and massless higher spin multiplets
• Adinkras for Clifford Algebras, and Worldline Supermultiplets
• A Lorentz Covariant Holoraumy-Induced "Gadget" From Minimal Off-Shell 4D, N = 1 Supermultiplets
• Pure and entangled N=4 linear supermultiplets and their one-dimensional sigma-models
• On General Off-Shell Representations of Worldline (1D) Supersymmetry
• Automorphism Properties of Adinkras
• Golden Ratio Controlled Chaos in Supersymmetric Dynamics
• 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
• Creating Infinitesimal Generators And Robust Messages With Adinkras
• Adinkras: Graphs of Clifford Algebra Representations, Supersymmetry, and Codes
• SUSY Equation Topology, Zonohedra, and the Search for Alternate Off-Shell Adinkras
• Spacetime Spin and Chirality Operators for Minimal 4D, $\mathcal{N}$ = 1 Supermultiplets From BC${}_4$ Adinkra-Tessellation of Riemann Surfaces
• The Spectrum Of Hypercubes Quotiented By Doubly Even Codewords And The Thermodynamics Of Adinkras