Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2002-04-02
Physics
High Energy Physics
High Energy Physics - Theory
Latex, 28 pages, Invited Lectures at ``The 22nd Winter School Geometry and Physics, Srni, Czech Republic, January 12-19, 2002.
Scientific paper
This set of lectures contain a brief review of some basic supersymmetry and its representations, with emphasis on superspace and superfields. Starting from the Poincar\'e group, the supersymmetric extensions allowed by the Coleman-Mandula theorem and its generalisation to superalgebras, the Haag, Lopuszanski and Sohnius theorem, are discussed. Minkowski space is introduced as a quotient space and Superspace is presented as a direct generalization of this. The focus is then shifted from a general presentation to the relation between supersymmetry and complex geometry as manifested in the possible target space geometries for N=1 and N=2 supersymmetric nonlinear sigma models in four dimensions. Gauging of isometries in nonlinear sigma models is discussed for these cases, and the quotient construction is described.
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