Model building in the free fermionic formulation of superstrings
Abstract (summary)
In this thesis we present results in the free fermionic formulation of string theory in four space-time dimensions as presented by I. Antoniadis and C. Bachas. First we discuss how to build N = 1 space-time supersymmetric models. We also use the low-energy requirements of N = 1 space-time supersymmetry as well as chiral space-time fermions to show that the spectrum does not contain any massless scalar fields which transform under the adjoint representation of the gauge group. We also discuss the consequences of these results for model building efforts.
In Chapter 1 and 2 we introduce the concepts of string theory as well as the notation which we will be using throughout the following chapters. In Chapter 3 we review the free fermionic formulation of string theory as presented by (AB) including the rules for model building. We first classify all the possible single boundary conditions for the free fermionic fields in the theory and then classify the cases for which two or more distinct boundary conditions are compatible.
In Chapter 4 we use the rules from Chapter 3 to construct several toy models, which show what possible gauge groups can arise in the theory and how they can be constructed. In Chapter 5 we use the classification of the boundary conditions for the fermionic fields to classify all the models with N = 4 spacetime supersymmetry. We then discuss the different possibilities to obtain models with N = 2, 1, and 0 space-time supersymmetry. We show that the requirement of N = 1 space-time supersymmetry severely restricts the allowed constructions of the world-sheet supercharge.
In Chapter 6 we prove, using the requirement of N = 1 space-time supersymmetry, that the spectrum does not contain any massless scalar fields transforming as the adjoint representation of the gauge group. Independently of this we also show that if we require chiral space-time fermions in the massless spectrum, then there are also no massless scalar fields transforming as the adjoint representation of the gauge group. These results have important implications for model building.