Free Fermionic Constructions of Heterotic Strings (2407.07034v1)

Abstract: This chapter is an introduction to the Free Fermionic Formulation of String Theory, with emphasis on heterotic model building. After a brief review of bosonization in two dimensional conformal field theories, we discuss how internal bosonic string coordinates can be consistently replaced by free fermionic degrees of freedom. In this framework, worldsheet supersymmetry may be realized entirely among free fermions. Embedding this construction into string theory leads to a number of constraints arising from modular invariance at one and higher genera. The solution of these constraints takes the form of a small number of model building rules from which the string spectrum and interactions may be analyzed. We review some of the most well-studied models in the literature and their classification, with emphasis on the symmetric basis. The explicit map of free fermionic models to the orbifold construction is presented in some detail.