Degenerate Geometries, Supersymmetry and Duality

Sammanfattning: String theory is a theory attempting to unify gravity with the electro-weak and strong interactions so successfully described by Quantum Field Theory. The implications of String Theory is not fully understood since it is still not a complete theory. For instance, until recently only perturbative aspects were investigated and recent strong coupling results indicate that it is part of a larger ``M-theory'' of which only certain limits are known. To gain more insight in the structure of String Theory it is useful to study some limiting cases. Another important tool is the web of duality transformations which relates different regimes of the theory.This thesis is concerned with both approaches mentioned above. First a bosonic string model with zero tension is examined, classically as well as quantum mechanically, using the BRST-method. A similar model for D-branes at strong coupling including supersymmetry is also constructed. These models are described by a degenerate geometry. Furthermore, some new 2D non-abelian dualities for massive excitations are found. Duality type transformations are then discussed in the context of 4D supergravity as a method for generating solutions.