Aspects of Grand Unification in Higher Dimensions

Abstract

We consider various aspects of string phenomenology in the context of heterotic orbifold constructions, where special emphasis is laid on the connection between GUT models in extra dimensions and their relation to string theory. We investigate orbifold models with more general structure than the Z_3 orbifold, on which most of the past research had focused. The picture of the heterotic brane world which naturally emerges allows us to make contact to field theoretic orbifold constructions in five and six dimensions, which have recently attracted much attention. We present a classification scheme for inequivalent orbifold models and apply the results to the case of Z_6-II point group. <br /> We develop the mathematical background for a stringy Higgs mechanism which allows us to lower the rank of the gauge group in the higher dimensions, which cannot be achieved by contemporary orbifold constructions. We provide all the calculational methods needed to unambiguously identify the gauge symmetry and to construct the matter representations.<br /> For specific model constructions, we focus on two promising gauge groups, namely on SO(10) and E_6. In the latter case, we derive a GUT model in six dimensions which has a Standard Model like gauge symmetry SU(3) x SU(2) x U(1) x U(1)' in four dimensions, and discuss its embedding into string theory.