Domain walls between gaugings in Maximal Supergravity

In this thesis, we explore domain wall solutions that interpolate between different gauge coupling values within a class of gauged maximal supergravity theories in four dimensions. We begin with a review of supergravity, superstring theories, and their interrelations. Following this, we discuss the gauging of supergravity using the embedding tensor formalism. We also outline the procedure of toroidal compactifications and briefly examine the connections between fluxes and gaugings. As an introductory step, we revisit the role of Romans' mass in ten-dimensional Type IIA massive supergravity and derive specific 1/2 BPS 8-brane solutions by solving the Killing spinor equations. In these solutions, Romans' mass behaves as a locally constant function, contributing to a discontinuity in the derivative of the harmonic function. We then reinterpret this computation within the framework of a particular gauging of four-dimensional maximal supergravity. Lastly, we extend our analysis by constructing a broader set of domain wall solutions linked to a family of CSO(p,q,r) gaugings, where different subsets of gauge couplings experience discontinuities across the domain wall.