New constraints on SO(10) model-building from string theory

A recent analysis of the methods by which higher-level gauge symmetries are realized in string theory has made it possible to systematically obtain new constraints on string GUT model-building. In this paper, we perform such a study for the case of SO(10) free-field string GUT models, and find a number of significant new results. First, we show that within the conventional string models using the so-called "diagonal" embeddings, all representations larger than the 16 must always transform as singlets under all gauge symmetries beyond SO(10). This includes the 45 and 54 representations, and holds regardless of the affine level at which SO(10) is realized. Furthermore, we show that such constructions can never give rise to the 120, 126, or 144 representations of SO(10) - again regardless of the affine level. We also perform a similar analysis for E₆, and find that the adjoint 78 representation must always transform as a singlet under all gauge symmetries beyond E₆; moreover, all representations beyond the 78 representation are prohibited. Taken together, these results thus severely limit the types of phenomenologically realistic field-theoretic SO(10) and E₆ models that can be obtained using such string constructions. Finally, we also explore the possibility of using non-diagonal free-field embeddings, and show that in the SO(10) case such embeddings may have improved phenomenological prospects.