Duality transformations in supersymmetric Yang-Mills theories coupled to supergravity

We consider dualitytransformations in N = 2, d = 4 Yang-Millstheorycoupled to N = 2 supergravity. A symplectic and coordinate covariant framework is established, which allows one to discuss stringy “classical and quantum duality symmetries” (monodromies), incorporating T- and S-dualities. In particular, we shall be able to study theories (like N = 2 heterotic strings) which are formulated in symplectic basis where a “holomorphic prepotential” F does not exist, and yet give general expressions for all relevant physical quantities. Dualitytransformations and symmetries for the N = 1 matter coupledYang-Millssupergravity system are also exhibited. The implications of duality symmetry on all N > 2 extended supergravities are briefly mentioned. We finally give the general form of the central charge and the N = 2 semiclassical spectrum of the dyonic BPS saturated states (as it comes by truncation of the N = 4 spectrum).