Dynamical supersymmetry breaking in four dimensions and its phenomenological implications

It is now established that the non-renormalization theorems are violated by non-perturbative effects in many four-dimensional supersymmetric theories, and that dynamical supersymmetry-breaking (DSB) occurs in some chiral gauge theories. Here we presenr a set of general techniques which allow one to determine whether or not supersymmetry is broken in almost any theory, and permit a quite detailed analysis of the dynamics of many theories. These techniques are illustrated by analysis of a wide variety of instructive models, including one in which DSB occurs and in which we compute the spectrum and ground state energy. A careful discussion of the prospects for realistic model building is presented, including: an argument that additional gauge interactions are required to build realistic theories; dynamical supersymmetry-breaking in N = 1 supergravity theories; a detailed discussion of the problems and prospects for dynamical supersymmetry-breaking in the multi-TeV energy range.