SPECIAL AND QUATERNIONIC ISOMETRIES - GENERAL COUPLINGS IN N = 2 SUPERGRAVITY AND THE SCALAR POTENTIAL

The general lagrangian for N = 2 matter-coupled supergravity is obtained, by gauging general isometries of quaternionic manifolds which can be coupled to supergravity. The resulting theories are purely geometrical and give an interplay between quaternionic and special Kahler geometry. The resulting scalar potential is expressed in terms of the two Killing prepotentials of the two geometries and it may be relevant to study transitions between different vacua in superstring theory. Furthermore from the geometrical point of view the prepotentials are hamiltonian functions yielding a poissonian realization of the gauge algebra on both the special Kahler and the quaternionic manifold. A possible cohomological obstruction to this realization is pointed out.