REALIZING HIGHER-LEVEL GAUGE SYMMETRIES IN STRING THEORY - NEW EMBEDDINGS FOR STRING GUTS

We consider the methods by which higher-level and non-simply laced gau ge symmetries can be realized in free-field heterotic string theory. W e show that all such realizations have a common underlying feature, na mely a dimensional truncation of the charge lattice, and we identify s uch dimensional truncations with certain irregular embeddings of highe r-level and non-simply laced gauge groups within level-one simply lace d gauge groups. This identification allows us to formulate a direct ma pping between a given subgroup embedding, and the sorts of GSO constra ints that are necessary in order to realize the embedding in string th eory. This also allows us to determine a number of useful constraints that generally affect string GUT model-building. For example, most str ing GUT realizations of higher-level gauge symmetries G(k) employ the so-called diagonal embeddings G(k) subset of G x G x ... x G. We find that there exist interesting alternative embeddings by which such grou ps can be realized at higher levels, and we derive a complete list of all possibilities for the GUT groups SU(5), SU(6), SO(10), and E(6) at levels k = 2,3,4 (and in some cases up to k = 7). We find that these new embeddings are always more efficient and require less central char ge than the diagonal embeddings which have traditionally been employed . As a by-product, we also prove that it is impossible to realize SO(1 0) at levels k > 4 in string theory. This implies, in particular, that free-field heterotic string models can never give a massless 126 repr esentation of SO(10).