Irreps and Off-shell Invariant Actions of the N-extended Supersymmetric Quantum Mechanics

Francesco Toppan

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arXiv · hep-th/0610180

Irreps and Off-shell Invariant Actions of the N-extended Supersymmetric Quantum Mechanics

Francesco Toppan

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Abstract

The complete classification of the irreducible representations of the N-extended one-dimensional supersymmetry algebra linearly realized on a finite number of fields is presented. Off-shell invariant actions of one-dimensional supersymmetric sigma models are constructed. The role of both Clifford algebras and the Cayley-Dickson's doublings of algebras in association with the N-extended supersymmetries is discussed. We prove in specific examples that the octonionic structure constants enter the N=8 invariant actions as coupling constants. We further explain how to relate one-dimensional supersymmetric quantum mechanical systems to the dimensional reduction of higher-dimensional supersymmetric theories.

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Francesco Toppan. 2006-10-16. Irreps and Off-shell Invariant Actions of the N-extended Supersymmetric Quantum Mechanics. https://arxiv.org/abs/hep-th/0610180

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