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A geometric formulation of supersymmetry. (English) Zbl 1371.81285

Summary: The scalar fields of supersymmetric models are coordinates of a geometric space. We propose a formulation of supersymmetry that is covariant with respect to reparametrizations of this target space. Employing chiral multiplets as an example, we introduce modified supersymmetry variations and redefined auxiliary fields that transform covariantly under reparametrizations. The resulting action and transformation laws are manifestly covariant and highlight the geometric structure of the supersymmetric theory. The covariant methods are developed first for general theories (not necessarily supersymmetric) whose scalar fields are coordinates of a Riemannian target space.

MSC:

81T60 Supersymmetric field theories in quantum mechanics
83E50 Supergravity
70S05 Lagrangian formalism and Hamiltonian formalism in mechanics of particles and systems
81R20 Covariant wave equations in quantum theory, relativistic quantum mechanics
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