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arXiv · hep-th/0409257

A geometric approach to scalar field theories on the supersphere

A. F. Schunck·Chris Wainwright
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Abstract

Following a strictly geometric approach we construct globally supersymmetric scalar field theories on the supersphere, defined as the quotient space $S^{2|2} = UOSp(1|2)/\mathcal{U}(1)$. We analyze the superspace geometry of the supersphere, in particular deriving the invariant vielbein and spin connection from a generalization of the left-invariant Maurer-Cartan form for Lie groups. Using this information we proceed to construct a superscalar field action on $S^{2|2}$, which can be decomposed in terms of the component fields, yielding a supersymmetric action on the ordinary two-sphere. We are able to derive Lagrange equations and Noether's theorem for the superscalar field itself.

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A. F. Schunck, Chris Wainwright. 2004-09-24. A geometric approach to scalar field theories on the supersphere. https://doi.org/10.1063/1.1850363

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