Elevating the Free-Fermion Z2× Z2 Orbifold Model to a Compactification of F-Theory
Per Berglund, John Ellis, Alon E. Faraggi, D. V. Nanopoulos, Zongan Qiu
Abstract
We study the elliptic fibrations of some Calabi-Yau three-folds, including the Z2× Z2 orbifold with (h1,1,h2,1)=(27,3), which is equivalent to the common framework of realistic free-fermion models, as well as related orbifold models with (h1,1,h2,1)=(51,3) and (31,7). However, two related puzzles arise when one considers the (h1,1,h2,1)=(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.
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