Constraints on grand unified superstring theories

We evaluate some constraints on the construction of grand unified superstring theories (GUSTs) using higher level Kac-Moody algebras on the world-sheet. In the most general formulation of the heterotic string in four dimensions, an analysis of the basic GUST model-building constraints, including a realistic hidden gauge group, reveals that there are no E6 models and any SO(10) models can only exist at level-5. Also, any such SU(5) models can exist only for levels 4≤k≤19. These SO(10) and SU(5) models risk having many large, massless, phenomenologically troublesome representations. We also show that with a suitable hidden sector gauge group, it is possible to avoid free light fractionally charged particles, which are endemic to string derived models. We list all such groups and their representations for the flipped SU(5)xU(1) model. We conclude that a sufficiently binding hidden sector gauge group becomes a basic model-building constraint. (orig.)