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On dimensional extension of supersymmetry: from worldlines to worldsheets. (English) Zbl 1286.81156

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.

MSC:

81T60 Supersymmetric field theories in quantum mechanics
81Q60 Supersymmetry and quantum mechanics
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