Realizing higherlevel gauge symmetries in string theory: new embeddings for string GUTs
Abstract
We consider the methods by which higherlevel and nonsimply laced gauge symmetries can be realized in freefield heterotic string theory. We show that all such realizations have a common underlying feature, namely a dimensional truncation of the charge lattice, and we identify such dimensional truncations with certain irregular embeddings of higherlevel and nonsimply laced gauge groups within levelone simply laced gauge groups. This identification allows us to formulate a direct mapping between a given subgroup embedding, and the sorts of GSO constraints that are necessary in order to realize the embedding in string theory. This also allows us to determine a number of useful constraints that generally affect string GUT modelbuilding. For example, most string GUT realizations of higherlevel gauge symmetries G_{k} employ the socalled diagonal embeddings G_{k} ∉ G × G × … × G. We find that there exist interesting alternative embeddings by which such groups 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 charge than the diagonal embeddings which have traditionally been employed. As a byproduct, we also prove that it is impossible to realize SO(10) at levels k > 4 in string theory. This implies, in particular, that freefield heterotic string models can never give a massless 126 representation of SO(10).
 Publication:

Nuclear Physics B
 Pub Date:
 February 1996
 DOI:
 10.1016/05503213(96)004063
 arXiv:
 arXiv:hepth/9604112
 Bibcode:
 1996NuPhB.479..113D
 Keywords:

 High Energy Physics  Theory;
 High Energy Physics  Phenomenology
 EPrint:
 69 pages, LaTeX, 5 figures (Encapsulated PostScript). Revised to match published version