Calabi-Yau four-folds for M- and F-theory compactifications

Abstract

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 nonperturbative 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.

Calabi-Yau fourfolds with flux and supersymmetry breaking

“…16 In order for these corrections to be negligible in the large volume limit, we have to demand that the invariants (3.43) are small for the Calabi-Yau fourfold, which in addition should have a large Euler number. In [16,36] the invariants (3.43) are given for some examples, showing that this requirement is a rather strong constraint. We have, however, found examples in which they are considerably smaller than the Euler number.…”

“…20 For a good collection of general topological properties of Calabi-Yau fourfolds see chapter 2 of [36]. 21 Here we make the choice T 2 = 1, i.e.…”

Modular amplitudes and flux-superpotentials on elliptic Calabi-Yau fourfolds

“…As far as the differential structure and some aspects of mirror symmetry are concerned this is based on the analysis of [7][8][9]. The analysis can be viewed as a generalization of the ones that lead to special geometry for Calabi-Yau threefolds [25] and was discussed with emphasis on mirror symmetry in [26].…”

“…We now study the fourfold X 24 which has been introduced in [9]. Its integrality and modular properties have been further discussed in [17,27].…”

“…Together with mirror symmetry this results in a large variety of geometrical tools that can be used to study the physically relevant structures on these moduli spaces. In this paper we want to improve on these tools following the line of the papers [7][8][9][10][11][12].…”