Institute of Theoretical Physics
Chalmers University of Technology and Göteborg University – Göteborg 1999
In recent years there has been a dramatic progress in the understanding of the non-perturbative structure of various physical theories.
In particular string theory has been vastly developed during these years, where a lot of duality conjectures between the different string theories have arisen.
The introductory text of this thesis is an attempt to describe this development in short and to make a brief overview of the subject.
Special focus is put on solitonic solutions in various field theories, which is the corner stone for these duality conjectures.
The introduction of supersymmetry is also essential for the understanding of duality by its natural way of handling BPS-states through the algebra.
In string theory, which is not only a supersymmetric theory but also includes gravity, these studies are put together through the discovery of various p-brane solutions to the background field equations.
The geometrical structure of these solutions is studied in some of the papers in this thesis.
In a generalization to the treatment of p-branes as solutions which break the local vacuum symmetry, the theory of almost product structures (APS-theory) has arisen as the natural candidate to the study of the intricate geometry of these solutions.
The last two papers deal with this ansatz where it is also seen that APS-theory is the most natural way of treating all kinds of splitting of manifolds including fibrations, Yang-Mills theoryand Kaluza-Klein theory.