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arXiv · hep-th/9812141

Elevating the Free-Fermion $Z_2\times Z_2$ Orbifold Model to a Compactification of F-Theory

Per Berglund·John Ellis·Alon E. Faraggi·D. V. Nanopoulos·Zongan Qiu
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Abstract

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.

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Per Berglund, John Ellis, Alon E. Faraggi, D. V. Nanopoulos, Zongan Qiu. 1999-08-29. Elevating the Free-Fermion $Z_2\times Z_2$ Orbifold Model to a Compactification of F-Theory. https://doi.org/10.1142/s0217751x00000598

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