Toward the classification of BPS solutions of N=2, d=5 gauged supergravity with matter couplings

Abstract

In this thesis I discuss the derivation of the BPS solutions of the most general N=2, d=5 gauged supergravity with matter. In particular I will concentrate on the dependence of BPS equations on the choice of the gauging, in presence of not trivial hypermultiplets (not constant prepotential). My purpose is, starting from the experience gained in some special examples, to extend the results of Gauntlett et Gutowski for the minimal gauged case to the theory with a generic number of hypermultiplets. Two ingredients are fundamental for this study: rewriting the BPS constraints on the killing spinor in term of bosonic quantities as first introduced in hep-th/0209114 and the analysis of hyperini equation.