Extended Geometry and Magical Supergravities

Abstract

During the last decades, double and exceptional field theory have been introduced in an attempt to understand the dualities of compactified supergravities from a geometrical perspective. There has been much work done on this subject where the exceptional field theories have been intended to understand the symmetries of M-theory. However, there exists another class of supergravities, which has deep ties to the Lie groups found in the magical square of Lie algebras, and which has yet to be understood to full extent. The aim of this thesis is to understand and develop a formalism using extended geometry for the non-gauged magical supergravities, more specifically the bosonic sector, in various external dimensions. This includes a systematic investigation of solutions of the section constraint for general real form of the internal structure algebra