20.500.12556/DKUM-86150 Machine learning and algebraic approaches towards complete matter spectra in 4d F-theory Strojno učenje in algebrični pristopi k izvedenim spektrom snovi v 4d F-teoriji Motivated by engineering vector-like (Higgs) pairs in the spectrum of 4d Ftheory 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 dP3, 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. Differential Geometry Algebraic Geometry F-Theory Flux Compactifications Field Theories Higher Dimensions Diferencialna geometrija algebraična geometrija teorija F kompaktifikacija pretoka teorije polja višje dimenzije true false true SISSA Angleški jezik Slovenski jezik Znanstveno delo 2023-10-13 12:02:05 2023-10-13 12:37:04 2023-10-16 09:23:57 0000-00-00 00:00:00 2021 0 0 71 str. Št. 1, št. članka 196 28. jan. 2021 0000-00-00 Zaloznikova Objavljeno NiDoloceno 2020-10-07 2020-12-14 2021-01-28 517.5 56548099 10.1007/JHEP01(2021)196 1029-8479 Machine_learning_and_algebraic_approaches_Bies_2021.pdf Machine_learning_and_algebraic_approaches_Bies_2021.pdf 1 C0392E1977496A9B0ED613E22B91DC57 368cd41ab73e41ec4fd9c333cca7644a1d0b68a90afe0f40510e080f57ee2567 98275b3c-69b4-11ee-b6cb-00155d000105 https://dk.um.si/Dokument.php?lang=slv&id=173551 https://doi.org/10.1007/JHEP01(2021)196 0 bdeb527d-69b4-11ee-b6cb-00155d000105 https://dk.um.si/Dokument.php?lang=slv&id=173552 Univerza v Mariboru 0 0 0