Part I. Superspace geometry: an approach to strings and supergravity super Yang-Mills theory. Part II. Aspects of string perturbation in supersymmetry preserving backgrounds

This thesis is divided into two parts. In the first part they present an on-shell formulation of ten-dimensional supergravity coupled to super Yang-Mills theory. They show that all the dynamics of this theory are embodied in a simple set of algebraic constraints on geometrical objects in superspace. They apply this formalism to study the propagation of the manifestly supersymmetric string in non-trivial vacua. The second part of the thesis is devoted to probing the structure of perturbation theory at arbitrary loop order for covariant fermionic strings. To start with they use conformal field theory techniques and complex function theory to calculate correlation functions of spin operators on arbitrary genus Riemann surfaces. These are then used to calculate the two fermion two boson and the four fermion scattering amplitudes at one loop. Finally they analyze the question of vacuum stability in string theories that start with tree level supersymmetry. They show that string theories that possess one or more U(1) factors with nonzero trace over the tree level fermion representation do generate at one loop Fayet-Iliopoulos D-terms. These have the effect of giving masses at one loop to various apriori massless fields and destabilize the vacuum by creating a dilaton-tadpole at two loops