Calabi-Yau fourfolds for M- and F-Theory compactifications

Details Calabi-Yau fourfolds for M- and F-Theory compactifications Calabi-Yau fourfolds for M- and F-Theory compactifications

1997-01-08

arxiv.org/abs/hep-th/9701023v2

Nucl.Phys.B518:515-574,1998

Physics

High Energy Physics

High Energy Physics - Theory

61 pages harvmac, one figure blow.eps, model 16 in tab 6.1 corrected and other minor corrections, references added

Scientific paper

10.1016/S0550-3213(97)00798-0

We investigate topological properties of Calabi-Yau fourfolds and consider a wide class of explicit constructions in weighted projective spaces and, more generally, toric varieties. Divisors which lead to a non-perturbative superpotential in the effective theory have a very simple description in the toric construction. Relevant properties of them follow just by counting lattice points and can be also used to construct examples with negative Euler number. We study nets of transitions between cases with generically smooth elliptic fibres and cases with ADE gauge symmetries in the N=1 theory due to degenerations of the fibre over codimension one loci in the base. Finally we investigate the quantum cohomology ring of this fourfolds using Frobenius algebras.

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