Thomas W. Grimm, Hirotaka Hayashi
We study the charged chiral matter spectrum of four-dimensional F-theory
compactifications on elliptically fibered Calabi-Yau fourfolds by using the
dual M-theory description. A chiral spectrum can be induced by M-theory
four-form flux on the fully resolved Calabi-Yau fourfold. In M-theory this flux
yields three-dimensional Chern-Simons couplings in the Coulomb branch of the
gauge theory. In the F-theory compactification on an additional circle these
couplings are only generated by one-loop corrections with charged fermions
running in the loop. This identification allows us to infer the net number of
chiral matter fields of the four-dimensional effective theory. The chirality
formulas can be evaluated by using the intersection numbers and the cones of
effective curves of the resolved fourfolds. We argue that a study of the
effective curves also allows to follow the resolution process at each
co-dimension. To write simple chirality formulas we suggest to use the
effective curves involved in the resolution process to determine the matter
surfaces and to connect with the group theory at co-dimension two in the base.
We exemplify our methods on examples with SU(5) and SU(5)xU(1) gauge group.
View original:
http://arxiv.org/abs/1111.1232
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