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

TL;DR

This paper explores the topological features of Calabi-Yau fourfolds relevant for M- and F-theory compactifications, focusing on their construction, divisors, gauge symmetries, and quantum cohomology.

Contribution

It provides explicit constructions of Calabi-Yau fourfolds in toric varieties, characterizes divisors for superpotential contributions, and analyzes transitions and quantum cohomology.

Findings

Divisors for superpotential are characterized by lattice point counting.

Constructed examples with negative Euler number.

Studied transitions between smooth and gauge-enhanced fibers.

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 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.