Root bundles and towards exact matter spectra of F-theory MSSMs
Abstract Motivated by the appearance of fractional powers of line bundles in studies of vector-like spectra in 4d F-theory compactifications, we analyze the structure and origin of these bundles. Fractional powers of line bundles are also known as root bundles and can be thought of as generalization...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2021-09-01
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| Series: | Journal of High Energy Physics |
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| Online Access: | https://doi.org/10.1007/JHEP09(2021)076 |
| _version_ | 1818559715227992064 |
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| author | Martin Bies Mirjam Cvetič Ron Donagi Muyang Liu Marielle Ong |
| author_facet | Martin Bies Mirjam Cvetič Ron Donagi Muyang Liu Marielle Ong |
| author_sort | Martin Bies |
| collection | DOAJ |
| description | Abstract Motivated by the appearance of fractional powers of line bundles in studies of vector-like spectra in 4d F-theory compactifications, we analyze the structure and origin of these bundles. Fractional powers of line bundles are also known as root bundles and can be thought of as generalizations of spin bundles. We explain how these root bundles are linked to inequivalent F-theory gauge potentials of a G 4-flux. While this observation is interesting in its own right, it is particularly valuable for F-theory Standard Model constructions. In aiming for MSSMs, it is desired to argue for the absence of vector-like exotics. We work out the root bundle constraints on all matter curves in the largest class of currently-known F-theory Standard Model constructions without chiral exotics and gauge coupling unification. On each matter curve, we conduct a systematic “bottom”-analysis of all solutions to the root bundle constraints and all spin bundles. Thereby, we derive a lower bound for the number of combinations of root bundles and spin bundles whose cohomologies satisfy the physical demand of absence of vector-like pairs. On a technical level, this systematic study is achieved by a well-known diagrammatic description of root bundles on nodal curves. We extend this description by a counting procedure, which determines the cohomologies of so-called limit root bundles on full blow-ups of nodal curves. By use of deformation theory, these results constrain the vector-like spectra on the smooth matter curves in the actual F-theory geometry. |
| first_indexed | 2024-12-14T00:29:09Z |
| format | Article |
| id | doaj.art-37cf252333474377b2240136a12eb9a2 |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-12-14T00:29:09Z |
| publishDate | 2021-09-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-37cf252333474377b2240136a12eb9a22022-12-21T23:24:55ZengSpringerOpenJournal of High Energy Physics1029-84792021-09-012021916510.1007/JHEP09(2021)076Root bundles and towards exact matter spectra of F-theory MSSMsMartin Bies0Mirjam Cvetič1Ron Donagi2Muyang Liu3Marielle Ong4Department of Mathematics, University of PennsylvaniaDepartment of Mathematics, University of PennsylvaniaDepartment of Mathematics, University of PennsylvaniaDepartment of Physics and Astronomy, University of PennsylvaniaDepartment of Mathematics, University of PennsylvaniaAbstract Motivated by the appearance of fractional powers of line bundles in studies of vector-like spectra in 4d F-theory compactifications, we analyze the structure and origin of these bundles. Fractional powers of line bundles are also known as root bundles and can be thought of as generalizations of spin bundles. We explain how these root bundles are linked to inequivalent F-theory gauge potentials of a G 4-flux. While this observation is interesting in its own right, it is particularly valuable for F-theory Standard Model constructions. In aiming for MSSMs, it is desired to argue for the absence of vector-like exotics. We work out the root bundle constraints on all matter curves in the largest class of currently-known F-theory Standard Model constructions without chiral exotics and gauge coupling unification. On each matter curve, we conduct a systematic “bottom”-analysis of all solutions to the root bundle constraints and all spin bundles. Thereby, we derive a lower bound for the number of combinations of root bundles and spin bundles whose cohomologies satisfy the physical demand of absence of vector-like pairs. On a technical level, this systematic study is achieved by a well-known diagrammatic description of root bundles on nodal curves. We extend this description by a counting procedure, which determines the cohomologies of so-called limit root bundles on full blow-ups of nodal curves. By use of deformation theory, these results constrain the vector-like spectra on the smooth matter curves in the actual F-theory geometry.https://doi.org/10.1007/JHEP09(2021)076F-TheoryDifferential and Algebraic Geometry |
| spellingShingle | Martin Bies Mirjam Cvetič Ron Donagi Muyang Liu Marielle Ong Root bundles and towards exact matter spectra of F-theory MSSMs Journal of High Energy Physics F-Theory Differential and Algebraic Geometry |
| title | Root bundles and towards exact matter spectra of F-theory MSSMs |
| title_full | Root bundles and towards exact matter spectra of F-theory MSSMs |
| title_fullStr | Root bundles and towards exact matter spectra of F-theory MSSMs |
| title_full_unstemmed | Root bundles and towards exact matter spectra of F-theory MSSMs |
| title_short | Root bundles and towards exact matter spectra of F-theory MSSMs |
| title_sort | root bundles and towards exact matter spectra of f theory mssms |
| topic | F-Theory Differential and Algebraic Geometry |
| url | https://doi.org/10.1007/JHEP09(2021)076 |
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