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BPS states of Fourfolds as candidates for Kaluza-Klein modes

Within the framework of the cosmological theory of the Big Bang, F-theory that unifies all four types of fundamental interactions is represented. Among the most exciting predictions of physics beyond the Standard Model is the assumption of the space of extra dimensions that solves the hierarchy problem. With the presence of this extra dimensions are connected the searches for Kaluza-Klein partners of gravitons, gauge bosons and microscopic black holes at the LHC. In the framework of F-theory, Calabi-Yau fourfold is considered as a space of extra dimensions. We study the duality between the F-theory compactified on the K3-surface and $E_8\times E_8$ heterotic string compactified on the torus, $T^2$. The set of BPS states corresponding to the Calabi-Yau fourfolds, which has either an elliptic curve or a K3-fibration as a layer, is studied in the aspect of correspondence to the KK modes of the M-theory on $R^8\times T^2 \times S^1 / Z_2$. The singularities of the moduli space of the Calabi-Yau fourfold make it possible to observe massive KK modes, the masses of which are obtained from the M-theory of supergravity. The result is of interest for a theoretical understanding of the KK modes, the experimental searches for which are carried out at the LHC.