2004/09/24 by A. F. Schunck, Chris Wainwright
Physics and Astronomy · #Action (physics) #Advanced Differential Geometry Research #Black Holes and Theoretical Physics #Connection (principal bundle) #Cosmology and Gravitation Theories #Field (mathematics) #Invariant (physics) #Lie group #Quotient #Scalar (mathematics) #Scalar field #Superspace #hep-th
paper · pdf · doi:10.1063/1.1850363
published as J.Math.Phys. 46 (2005) 033511 · 38 pages, 1 figure
arxiv created 2004/09/24 · openalex publication_date 2005/02/11 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
Following a strictly geometric approach we construct globally supersymmetric scalar field theories on the supersphere, defined as the quotient space S2∣2=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 S2∣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.