New deformations of N=2 supergravity

Abstract

Supergravity is a field theory that combines general relativity with local supersymmetry. It serves as a framework for studying a large variety of phenomena, such as black holes and cosmology. Supergravity also describes the low-energy degrees of freedom associated with string theory, which has been proposed as a consistent theory of quantum gravity. In this thesis we study new deformations of N=2 supergravity in four space-time dimensions. One class of deformations we consider consists of gauge deformations. Applying the so-called embedding tensor formalism, we present general gauge deformations of N=2 supergravity, which, due to the presence of electric/magnetic duality, lead to the introduction of both electric and magnetic charges. As an application we briefly review partial supersymmetry breaking in maximally symmetric space-times in the presence of general gaugings. We confirm the result found in previous literature, that in a Minkowski background, partial supersymmetry breaking is only possible in the presence of magnetic charges. As a new application we study possible supersymmetric solutions in space-times that describe the near-horizon geometry of a static black hole. We find two classes of solutions. One is fully supersymmetric. It contains the near-horizon solution of ungauged supergravity that appears for BPS black holes. The other class exhibits four supersymmetries. It contains near-horizon solutions of BPS black holes in N=2 gauged supergravity. Other deformations we consider in this thesis are supersymmetric higher-derivative couplings. These couplings play an important role as next-to-leading order corrections to low-energy effective actions of string theory. In this thesis we introduce a systematic procedure to construct a large variety of new higher-derivative deformations in N=2 supergravity. We study the possible contribution of these new couplings to the entropy and the electric charges of BPS black holes. We derive a 'non-renormalization' theorem according to which these contributions vanish.