Weaving Worldsheet Supermultiplets from the Worldlines Within

Abstract

Using the fact that every worldsheet is ruled by two (light-cone) copies of worldlines, the recent classification of off-shell supermultiplets of N-extended worldline supersymmetry is extended to construct standard off-shell and also unidextrous (on the half-shell) supermultiplets of worldsheet (p,q)-supersymmetry with no central extension. In the process, a new class of error-correcting (even-split doubly-even linear block) codes is introduced and classified for $p+q\le 8$, providing a graphical method for classification of such codes and supermultiplets. This also classifies quotients by such codes, of which many are not tensor products of worldline factors. Also, supermultiplets that admit a complex structure are found to be depictable by graphs that have a hallmark twisted reflection symmetry.

Extended version, with added discussion of complex and quaternionic tensor products demonstrating that certain quotient supermultiplets do not factorize over any ground field

References in corpus (12)

• Refining the classification of the irreps of the 1D N-Extended Supersymmetry
• Codes and Supersymmetry in One Dimension
• Spin Holography via Dimensional Enhancement
• Relating Doubly-Even Error-Correcting Codes, Graphs, and Irreducible Representations of N-Extended Supersymmetry
• On non-minimal N=4 supermultiplets in 1D and their associated sigma-models
• Adinkras for Clifford Algebras, and Worldline Supermultiplets
• 4D, N = 1 Supersymmetry Genomics (II)
• 4D, N=1 Supergravity Genomics
• Pure and entangled N=4 linear supermultiplets and their one-dimensional sigma-models
• Golden Ratio Controlled Chaos in Supersymmetric Dynamics
• Superspace: a Comfortably Vast Algebraic Variety
• Worldsheet Matter Superfields on Half-Shell

Cited by in corpus (6)

• On Clifford-Algebraic "Holoraumy", Dimensional Extension, and SUSY Holography
• Golden Ratio Controlled Chaos in Supersymmetric Dynamics
• Adinkra Height Yielding Matrix Numbers: Eigenvalue Equivalence Classes for Minimal Four-Color Adinkras
• Properties of HYMNs in Examples of Four-Color, Five-Color, and Six-Color Adinkras
• On Supermultiplet Twisting and Spin-Statistics
• Structural Theory of 2-d Adinkras