GUT relations from string theory compactifications

Wilson line on a non-simply connected manifold is a nice way to break SU(5) unified symmetry, and to solve the doublet-triplet splitting problem. This mechanism also requires, however, that the two Higgs doublets are strictly vector-like under all underlying gauge symmetries. and consequently there is a limit in a class of modes and their phenomenology for which the Wilson line can be used. An alternative is to turn on a non-flat line bundle in the U(1)gamma direction on an internal manifold, which does not have to be non-simply connected. The U(1)gamma gauge field has to remain in the massless spectrum, and its coupling has to satisfy the GUT relation. In string theory compactifications, however. it is not that easy to satisfy these conditions in a natural ways we call it U(1)gamma problem. In this article, we explain how the problem is solved in some parts of moduli space of string theory compactifications. Two major ingredients are an extra strongly coupled U(1) gauge field and parametrically large volume for compactification, which is also essential in accounting for the hierarchy between the Planck scale and the GUT scale. Heterotic M-theory vacua and F-theory vacua are discussed. This article also shows that the toroidal orbifold GUT approach using discrete Wilson lines corresponds to the non-flat line-bundle breaking above when orbifold singularities are blown up. Thus, the orbifold GUT approach also suffers from the U(1)gamma problem, and Lhis article shows how to fix it. (c) 2008 Elsevier B.V. All rights reserved.