Heterotic strings in symmetric and asymmetric orbifold backgrounds

Spectra in Standard-like Z3 Orbifold Models

“…In Pattern 1.2, the SO(10) matter is in 16s, which have as their lowest dimensional invariant (16) 4 . To have effective vector masses for these states from superpotential terms would require breaking SO (10). We leave these issues to further research.…”

“…Communication via U (1)s was for example noted in Refs. [10,51,52], while the occurence of states in nontrivial representations of both observable and hidden nonabelian factors has been noted in other orbifold constructions, for example in a Z 3 × Z 3 model in Ref. [46].…”

“…Consistency conditions [10,38] for {V, a 1 , a 3 , a 5 } following from the homomorphism condition (2.23) have been accounted for in the embeddings enumerated in [24]. For example, (θ, n 1 e 1 + n 3 e 3 + n 5 e 5 ) 3 = (1, 0) implies that we must have…”

“…The results of a detailed study of these aspects of the underlying string theory [10,38] have been built into the embeddings given in [24] and the recipes given below. As noted above, the boundary conditions are labeled by the conjugacy classes of the space group; it is clear that in the general case, the extension U in (2.22)-and more specifically the embedding E(n 1 , n 3 , n 5 )-will be different for each conjugacy class.…”

“…Similarly realistic four-dimensional bosonic heterotic string models have not yet been engineered, though the foundations of such an effort were laid some time ago [2,3,9,10]. Some of the most promising models were of the Z 3 orbifold variety, with nonvanishing Wilson lines (discussed below) chosen such that the matter spectrum naturally had three generations.…”