Patterns in Calabi–Yau Distributions

Abstract

Abstract:We explore the distribution of topological numbers in Calabi-Yau manifolds, using the Kreuzer-Skarke dataset of hypersurfaces in toric varieties as a testing ground. While the Hodge numbers are well-known to exhibit mirror symmetry, patterns in frequencies of combination thereof exhibit striking new patterns. We find pseudo-Voigt and Planckian distributions with high confidence and exact fit for many substructures. The patterns indicate typicality within the landscape of Calabi-Yau manifolds of various dimension.

Calabi–Yau Volumes and Reflexive Polytopes

“…We summarize the above two constructions in Figure 3. While there has been a host of activity following Batyrev-Borisov and Kreuzer-Skarke in studying the distribution of the topological quantities of compact Calabi-Yau hypersurfaces [6,[9][10][11][12][59][60][61][62][63][64], in this paper we will be exclusively concerned with the arrow to the right in the figure and study the affine Calabi-Yau (n + 1)-fold X , as a complex cone over the Gorenstein Fano variety X(∆ n ) where ∆ n is reflexive. For convenience, we will use ∆ n−1 so that X is of complex dimension n. A key fact is that X is itself a real cone over a Sasaki-Einstein manifold Y of (real) dimension 2n − 1.…”

Orientifold Calabi-Yau threefolds with divisor involutions and string landscape

“…In most of these approaches, finding Calabi-Yau threefolds with a non-trivial odd cohomology h 1,1 − (X/σ * ) is a crucial ingredient. A great deal of progress has been made in understanding the statistical structure of the moduli in many classes of Calabi-Yau threefolds, by brute force calculation and scans, without considering the orientifold involution explicitly, and how this relates to properties such as the axion landscape or Swiss cheese structure [54][55][56][57][58][59][60][61]. Recently, in the context of Complete Intersection Calabi-Yau 3-folds (CICYs) embedded in products of projective spaces [62], a landscape of orientifold vacua has been constructed [63,64] from the most favorable description of the CICY 3-folds database [65].…”

The Calabi-Yau Landscape: from Geometry, to Physics, to Machine-Learning

“…It is also curious to note that (27,27) is the most occupied point: with a multiplicity of 910113. The distribution of the Hodge numbers follows pseudo-Voigt/Planickian curves and is the subject of [100].…”