On dimensional extension of supersymmetry: from worldlines to worldsheets (Q361178)

The paper studies the extension of off-shell worldline supersymmetries to off-shell worldsheet \((p,q)\)-supersymmetries and identifies an obstruction specified by a theorem that can be formulated graphically as the exclusion of a certain type of ``Adinkra'' (a graphical representation of algebraic structures found in all unconstrained supersymmetric quantum-mechanical systems) or computationally as a spin sum rule. Evasion of this obstruction is both sufficient and necessary for the extension from \(0+1\) to \(1+1\) dimensions and indeed expected to produce all off-shell \((p,q)\)-supermultiplets, but not sufficient for the extension to higher dimensions.