Machine learning and algebraic approaches towards complete matter spectra in 4d F-theory

• Main Authors: Martin Bies, Mirjam Cvetič, Ron Donagi, Ling Lin, Muyang Liu, Fabian Ruehle
• Format: Article
• Language: English
• Published: SpringerOpen 2021-01-01
• Series: Journal of High Energy Physics
• Subjects: Differential and Algebraic Geometry; F-Theory; Flux compactifications; Field Theories in Higher Dimensions
• Online Access: https://doi.org/10.1007/JHEP01(2021)196

Abstract Motivated by engineering vector-like (Higgs) pairs in the spectrum of 4d F-theory compactifications, we combine machine learning and algebraic geometry techniques to analyze line bundle cohomologies on families of holomorphic curves. To quantify jumps of these cohomologies, we first generate 1.8 million pairs of line bundles and curves embedded in dP 3, for which we compute the cohomologies. A white-box machine learning approach trained on this data provides intuition for jumps due to curve splittings, which we use to construct additional vector-like Higgs-pairs in an F-Theory toy model. We also find that, in order to explain quantitatively the full dataset, further tools from algebraic geometry, in particular Brill-Noether theory, are required. Using these ingredients, we introduce a diagrammatic way to express cohomology jumps across the parameter space of each family of matter curves, which reflects a stratification of the F-theory complex structure moduli space in terms of the vector-like spectrum. Furthermore, these insights provide an algorithmically efficient way to estimate the possible cohomology dimensions across the entire parameter space.