Studies of low-energy effective actions in supersymmetric field theories

This thesis examines low-energy effective actions of supersymmetric quantum field theories. These effective actions contain information about the low-energy eld content and dynamics of quantum field theories and are essential for understanding their phenomenological and theoretical properties. In chapters 2 to 5, the covariant background field method is used to investigate quantum corrections to sectors of the low-energy effective actions for a variety of supersymmetric field theories at one- and two-loops. We start by looking at the background field quantisation of a general N = 1 super-Yang-Mills theory and rederiving the well known one-loop finiteness conditions. This is followed by a reexamination of the effective potential of the simplest supersymmetric quantum field theory, the Wess-Zumino model. Next, the two-loop Euler-Heisenberg effective action is constructed for N = 1 supersymmetric quantum electrodynamics. This is a natural object to study in the progression of such two-loop Euler-Heisenberg calculations and is only the second such result using superfields. The theory is renormalised and the self-dual limit of the renormalised effective action is given explicitly in terms of digamma functions. The final quantum effective action studied is the two-loop Kahler potential for B-deformed N = 4 super-Yang-Mills theory. This sector of the effective action is purely a product of the deformation and its finiteness is demonstrated in a general background before specialising to give explicit results for two special cases. Chapter 6 studies spontaneously broken supersymmetry and, in particular, the pure Goldstino action. This is a universal sector of the low-energy effective action of any theory with spontaneously broken supersymmetry.