Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1998-12-17
Int.J.Mod.Phys.A15:1345-1362,2000
Physics
High Energy Physics
High Energy Physics - Theory
19 pages. Standard Latex. The lack of global section for the (27,3) model is emphasized, as well as a possible relation with t
Scientific paper
10.1142/S0217751X00000598
We study the elliptic fibrations of some Calabi-Yau three-folds, including the $Z_2\times Z_2$ orbifold with $(h_{1,1},h_{2,1})=(27,3)$, which is equivalent to the common framework of realistic free-fermion models, as well as related orbifold models with $(h_{1,1},h_{2,1})=(51,3)$ and (31,7). However, two related puzzles arise when one considers the $(h_{1,1},h_{2,1})=(27,3)$ model as an F-theory compactification to six dimensions. The condition for the vanishing of the gravitational anomaly is not satisfied, suggesting that the F-theory compactification does not make sense, and the elliptic fibration is well defined everywhere except at four singular points in the base. We speculate on the possible existence of N=1 tensor and hypermultiplets at these points which would cancel the gravitational anomaly in this case.
Berglund Per
Ellis John
Faraggi Alon E.
Nanopoulos Dimitri V.
Qiu Zongan
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