Heterotic string models with GUT gauge group SO(10)

Abstract

In this diploma thesis we investigate heterotic string models with N=(0,2) worldsheet supersymmetry and GUT gauge group SO(10). In this context we discuss the generalization of the heterotic (0,2) conformal field theory/geometry correspondence to the non-rational realm. In order to test the conjecture we develop tools for computing the charged massless non-singlet matter spectrum by making use of the powerful simple current formalism and its relation to orbifolds with discrete torsion. We use the extended Poincaré polynomial and the complementary Poincaré polynomial in order to count the number of generations, antigenerations and vectors for several rational and non-rational Landau-Ginzburg models. As a check of our counting algorithm we compare these numbers in the rational case with spectra computed by Blumenhagen-Wißkirchen. In order to test the generalization of the heterotic (0,2) CFT/geometry conjecture to the non-rational realm we compare our predictions for generations and antigenerations with the results from elliptic genera of Dister-Kachru models. Furthermore, we also predict the number of vectors in the non-rational case. Heterotic (0,2) model building is an interesting topic in its own right as this class of models provides a playground for phenomenologically interesting low-energy particle physics such as models with three particle generations. Our construction might be used in further work to study models with smaller gauge groups such as SU(5) or even SU(3) x SU(2).