ABSTRACT

This chapter introduces some of the arguments that have been used successfully to obtain exact information about strongly coupled field theories. Minimizing the generalized kinetic energy term implies that in the vacuum the scalars should all be constant. Electric-magnetic duality transformations are not symmetry transformations since they acts on the couplings. In general the total moduli space of a given theory need not be a smooth manifold; it may have “jumps” where submanifolds of different dimensions meet. Classically this occurs as a result of the Higgs mechanism: a charged scalar vev Higgses some vector multiplets, typically lifting them. More systematic control over the construction of rigid special Kahler (RSK) geometries is obtained by specializing to classes of RSK manifolds whose geometry can be naturally encoded in simpler structures. The chapter analyses one reformulation of RSK geometry which, when combined with some string theory ideas, has allowed a more systematic approach.