A geometric approach to scalar field theories on the supersphere
نویسندگان
چکیده
Following a strictly geometric approach we construct globally supersymmetric scalar field theories on the supersphere, defined as the quotient space S = UOSp(1|2)/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, 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. PACS numbers: 11.30.Pb, 12.60.Jv
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