Vector multiplets in N=2 supersymmetry and its associated moduli spaces

Abstract

An introduction to $N=2$ rigid and local supersymmetry is given. The construction of the actions of vector multiplets is reviewed, defining special Kähler manifolds. Symplectic transformations lead to either isometries or symplectic reparametrizations. Writing down a symplectic formulation of special geometry clarifies the relation to the moduli spaces of a Riemann surface or a Calabi-Yau 3-fold. The scheme for obtaining perturbative and non-perturbative corrections to a supersymmetry model is explained. The Seiberg-Witten model is reviewed as an example of the identification of duality symmetries with monodromies and symmetries of the associated moduli space of a Riemann surface.

40 pages, latex, no figures. Lectures given in the 1995 Trieste summer school in high energy physics and cosmology. Minor corrections and 1 reference added

References in corpus (2)

• A Search for Non-Perturbative Dualities of Local $N=2$ Yang--Mills Theories from Calabi--Yau Threefolds
• Special geometry and symplectic transformations

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