TY - JOUR

T1 - Realizing higher-level gauge symmetries in string theory

T2 - New embeddings for string GUTs

AU - Dienes, Keith R.

AU - March-Russell, John

N1 - Funding Information:
We wish to thank Alon Faraggi for initial collaborations, and for discussions throughout. We also thank P. Argyres, K.S. Babu, S. Chaudhuri, S.-W. Chung, A. Font, J. Lykken, E Wilczek, and E. Witten for helpful comments. This work was supported in part by DOE Grant No. DE-FG-0290ER40542 and by the W.M. Keck Foundation.

PY - 1996/11/11

Y1 - 1996/11/11

N2 - We consider the methods by which higher-level and non-simply laced gauge symmetries can be realized in free-field 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 higher-level and non-simply laced gauge groups within level-one 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 model-building. For example, most string GUT realizations of higher-level gauge symmetries Gk employ the so-called diagonal embeddings Gk ⊂ 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 E6 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 by-product, we also prove that it is impossible to realize SO(10) at levels k > 4 in string theory. This implies, in particular, that free-field heterotic string models can never give a massless 126 representation of SO(10).

AB - We consider the methods by which higher-level and non-simply laced gauge symmetries can be realized in free-field 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 higher-level and non-simply laced gauge groups within level-one 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 model-building. For example, most string GUT realizations of higher-level gauge symmetries Gk employ the so-called diagonal embeddings Gk ⊂ 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 E6 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 by-product, we also prove that it is impossible to realize SO(10) at levels k > 4 in string theory. This implies, in particular, that free-field heterotic string models can never give a massless 126 representation of SO(10).

UR - http://www.scopus.com/inward/record.url?scp=0030580253&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0030580253&partnerID=8YFLogxK

U2 - 10.1016/0550-3213(96)00406-3

DO - 10.1016/0550-3213(96)00406-3

M3 - Article

AN - SCOPUS:0030580253

SN - 0550-3213

VL - 479

SP - 113

EP - 172

JO - Nuclear Physics B

JF - Nuclear Physics B

IS - 1-2

ER -