SOLUTIONS OF N=2 GAUGED SUPERGRAVITY IN 4, 5 AND 6 DIMENSIONS

The main goal of the work we are presenting is the exploration of some sectors of the space of the supersymmetric solutions of supergravity theories with 8 supercharges, in 4, 5 and 6 dimensions, which led to the new solutions. We are firstly reviewing the supergravity theories of our interest, paying attention to their geometrical structure and to their possible gaugings. While discussing the 4-dimensional case, we are also introducing a couple of solutions generating techniques. We then introduce the idea of dimensionally reducing a theory and its solutions on a circle, as the necessary tool to relate 4, 5 and 6-dimensional ungauged supergravity theories among themselves. An interesting feature emerges from this treatment: there are two classes of 6-dimensional theories that lead, when compactified, to the same 5-dimensional model; the two 6-dimensional theories are therefore dual. In the present context, the main reason to treat dimensional reduction is given by the possibility of generating new solutions, reducing or uplifting known ones. Finally, we apply these techniques to generate the first 4-dimensional solution of U(1)-Fayet-Iliopoulos gauged supergravity coupled to vector multiplets, whose scalars parametrize a non-homogeneous Kähler manifold. It is a black hole solution, with AdS₄ asymptotes. We then explore the SU(2)-Fayet-Iliopoulos gauged sector, in 4 dimensions. Once a simple model is chosen, some solutions for this setting are found. More solutions for the same theory are obtained through dimensional reduction -that has been generalized to relate gauged theories- of a couple of known solutions for the 6-dimensional, FI-gauged theory. 5-dimensional solutions are obtained in the procedure, as well. Finally, a known 5-dimensional solution, an extremal black hole sourced by a BPST instanton, is uplifted to 6 dimensions.