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Adinkras and the dynamics of superspace prepotentials. (English) Zbl 1148.81013
Summary: We demonstrate a method for describing one-dimensional $N$-extended supermultiplets and building supersymmetric actions in terms of unconstrained prepotential superfields, explicitly working with the Scalar supermultiplet. The method uses intuitive manipulations of Adinkras and ${\cal{GR}}(d,N)$ algebras, a variant of Clifford algebras. In the process we clarify the relationship between Adinkras, ${\cal{GR}}(d,N)$ algebras, and superspace.

81Q60Supersymmetry and quantum mechanics
15A66Clifford algebras, spinors
70S05Lagrangian formalism and Hamiltonian formalism