Line bundle cohomologies on CICYs with Picard number two

Abstract

We analyse line bundle cohomologies on all favourable co-dimension two Complete Intersection Calabi Yau (CICY) manifolds of Picard number two. Our results provide further evidence that the cohomology dimensions of such line bundles are given by analytic expressions, which change between regions in the line bundle charge space. This agrees with recent observations of CY line bundles presented in Refs [1,2]. In many cases, the expressions for bundle cohomology dimensions are polynomial functions of the line bundle charges (of degree at most 3), and the regions are cones. A more novel observation is that for some CICY manifolds, the cohomologies are more succinctly determined by recursive relationships. There can also be boundaries between regions where a polynomial fit fails, and we link these exceptional cases to irregular behaviour of the index of the line bundle. Finally, our observations provide evidence for similarities in the line bundle cohomologies for CICY manifolds that share rows in the configuration matrix. Among such related CICY manifolds, we find both that the line bundle charge space is partitioned in the same manner, and that the same, or closely related, analytical descriptions apply for the cohomology dimensions in these regions.

arXiv commentv2: fixed references; 27 pages, 10 figures, python package

References in corpus (13)

• Heterotic Line Bundle Standard Models
• A Comprehensive Scan for Heterotic SU(5) GUT models
• Cohomology of Line Bundles: A Computational Algorithm
• On Free Quotients of Complete Intersection Calabi-Yau Manifolds
• Monad Bundles in Heterotic String Compactifications
• Evolving neural networks with genetic algorithms to study the String Landscape
• Machine Learning CICY Threefolds
• Stabilizing the Complex Structure in Heterotic Calabi-Yau Vacua
• Branes with Brains: Exploring String Vacua with Deep Reinforcement Learning
• Machine Learning Line Bundle Cohomologies of Hypersurfaces in Toric Varieties
• The Moduli Space of Heterotic Line Bundle Models: a Case Study for the Tetra-Quadric
• Yang-Mills Equations of Motion for the Higgs Sector of SU(3)-Equivariant Quiver Gauge Theories
• Interferometry with Synthetic Gauge Fields

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