Study of the BPS solution in N=4 gauged supergravity

Abstract

The study of static, spherically symmetric, and purely magnetic solutions of SU(2)xSU(2) gauge supergravity in four dimensions reveals solutions which preserve 1/4 of the supersymmetries. Among these solutions, there is a solution which is characterized by a BPS-monopole-type gauge field and a globally hyperbolic, everywhere regular geometry. It presents the first known example of non-Abelian backgrounds in gauge supergravity and in leading order effective string theory. One can verify that it also satisfies the corresponding field equations. In this thesis we study the geodesic motion for this solution. Moreover, we investigate its stability under linear, spherically symmetric, time-dependent perturbations. At present there are very few stable solutions. The exact BPS solution is expected because of the presence of unbroken supersymmetry generators. We show that the stability problem can be transformed into an eigenvalue problem which can be investigated numerically later on.