Topological invariants and fibration structure of complete intersection Calabi-Yau four-folds

Abstract

Abstract:We investigate the mathematical properties of the class of Calabi-Yau fourfolds recently found in ref. [1]. This class consists of 921,497 configuration matrices which correspond to manifolds that are described as complete intersections in products of projective spaces. For each manifold in the list, we compute the full Hodge diamond as well as additional topological invariants such as Chern classes and intersection numbers. Using this data, we conclude that there are at least 36,779 topologically distinct manifolds in our list. We also study the fibration structure of these manifolds and find that 99.95 percent can be described as elliptic fibrations. In total, we find 50,114,908 elliptic fibrations, demonstrating the multitude of ways in which many manifolds are fibered. A sub-class of 26,088,498 fibrations satisfy necessary conditions for admitting sections. The complete data set can be downloaded here.

Modularity from monodromy

“…The asymptotic behaviour of the central charge of a B-brane F • in the limit of large volume can be calculated using the Γ-class formula [47] 4) where in terms of the Chern classes c 2 , c 3 of M Γ C (M ) = 1 + 1 24…”

Jumping spectra and vanishing couplings in heterotic Line Bundle Standard Models

“…We will consider a particular existent Line Bundle Standard Model data set [19,20] built over Calabi-Yau manifolds which can be described as quotients of complete intersections in products of projective spaces (CICYs) [70][71][72][73][74][75][76]. Note that analogous constructions could be pursued over different base spaces, such as quotients of gCICYs [77] or toric hypersurfaces [78][79][80][81][82].…”

Mirror symmetry and elliptic Calabi-Yau manifolds

“…The largest known set of Calabi-Yau threefolds are constructed from the class of over 400 million reflexive 4D polytopes found by Kreuzer and Skarke [5,6], and exhibit this mirror symmetry structure. More recently, an increasing body of evidence [7][8][9][10][11][12][13][14][15][16] suggests that a large fraction of known Calabi-Yau threefolds have the property that they can be described as genus one or elliptic fibrations over a complex two-dimensional base surface. We recently showed that this is true of all but at most 4 Calabi-Yau threefolds in the Kreuzer-Skarke database having one or the other Hodge number h 2,1 , h 1,1 at least 140, and that at small h 1,1 the fraction of polytopes in the Kreuzer-Skarke database that lack an obvious elliptic or genus one fibration decreases roughly as 0.1 × 2 5−h 1,1 .…”