| Title: | Machine learning and algebraic approaches towards complete matter spectra in 4d F-theory |
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| Authors: | ID Bies, Martin (Author)
ID Cvetič, Mirjam (Author)
ID Donagi, Ron (Author)
ID Lin, Ling (Author)
ID Liu, Mingqiang (Author)
ID Ruehle, Fabian (Author) |
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| Files: |  Machine_learning_and_algebraic_approaches_Bies_2021.pdf (889,92 KB)
MD5: C0392E1977496A9B0ED613E22B91DC57
 https://doi.org/10.1007/JHEP01(2021)196
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| Language: | English |
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| Work type: | Scientific work |
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| Typology: | 1.01 - Original Scientific Article |
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| Organization: | UM - University of Maribor
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| Abstract: | 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. |
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| Keywords: | Differential Geometry, Algebraic Geometry, F-Theory, Flux Compactifications, Field Theories, Higher Dimensions |
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| Publication status: | Published |
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| Publication version: | Version of Record |
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| Submitted for review: | 07.10.2020 |
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| Article acceptance date: | 14.12.2020 |
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| Publication date: | 28.01.2021 |
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| Publisher: | SISSA |
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| Year of publishing: | 2021 |
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| Number of pages: | 71 str. |
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| Numbering: | Št. 1, št. članka 196 |
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| PID: | 20.500.12556/DKUM-86150  |
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| UDC: | 517.5 |
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| ISSN on article: | 1029-8479 |
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| COBISS.SI-ID: | 56548099 |
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| DOI: | 10.1007/JHEP01(2021)196 |
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| Publication date in DKUM: | 13.10.2023 |
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| Views: | 480 |
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| Downloads: | 47 |
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| Metadata: |    |
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| Categories: | Misc.
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