A geometric approach to scalar field theories on the supersphere

Details A geometric approach to scalar field theories on the supersphere A geometric approach to scalar field theories on the supersphere

2004-09-24

arxiv.org/abs/hep-th/0409257v1

J.Math.Phys. 46 (2005) 033511

Physics

High Energy Physics

High Energy Physics - Theory

38 pages, 1 figure

Scientific paper

10.1063/1.1850363

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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